A1 MNLEAN881263 FIF1 - Mr. Davenport's Math … greater than 1. The domain is the set of integers n...

Name ________________________________________ Date ___________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

Algebra 1 57 Common Core Assessment Readiness

F.IF.1

SELECTED RESPONSE Select the correct answer.

1. What are the domain and range of the function y = f (x) as shown on the graph?

The domain is {0.25,0.5,1, 2, 4,8} ,

and the range is {−3,− 2,−1,0,1, 2} .

The domain is {−3,− 2,−1,0,1, 2} and

the range is {0.25,0.5,1, 2, 4,8} .

The domain is all real numbers between −3 and 2, and the range is

all real numbers between 0.25 and 8.

The domain is all real numbers

between 0.25 and 8, and the range is all real numbers between −3 and 2.

2. The linear function f (x) has the domain

x ≥ 5. Which of the following does not

represent an element of the range?

f 2 1

2⎛⎝⎜

⎞⎠⎟

f (5)

f (10.5868)

f (100,000)

Select all correct answers.

3. The domain of the function f(x) is the set

of integers greater than −5. Which of the following values represent elements of the range of f?

f (4.8) f 1

2⎛⎝⎜

⎞⎠⎟

f (−2) f (0)

f (−5) f (14)

f (8) f (−18)

CONSTRUCTED RESPONSE

4. Examine the two sets below. The first is

the set of months in the year and the second is the possible numbers of days per month. Is the relation that maps the

month to its possible number of days a function? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. Does the table represent a function? If so, state the domain and range.

If not, state why.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. The graph of y = − 1

2x + 3 is shown

below. Use the graph to find the y-values associated with x = −2, x = 0, and x = 2. If y = f(x) is a function, which of the

values given above are in the range and which are in the domain?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

7. An exponential function y = f(x) is graphed below. The graph has a

horizontal asymptote at y = −3. What are the domain and range of f(x)?

________________________________________

________________________________________

8. Determine whether the following

situations represent functions. Explain your reasoning. If the situation represents a function, give the domain and range.

a. Each U.S. coin is mapped to its monetary value.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. A $1, $5, $10, $20, $50, or $100 bill

is mapped to all the sets of coins that are the same total value as the bill.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

x f(x) −2 2

−1 6

0 10

1 14

2 18

Name ________________________________________ Date ___________________ Class __________________



F.IF.2


1. What is the value of the function

f(x) = x2 − 5x + 2 evaluated at x = 2?

−4

2

6

16

2. Joshua is driving to the store. The

average distance d, in miles, he travels over t minutes is given by the function

d(t) = 0.5t. What is the value of the function when t = 15?

75 miles

7.5 minutes

7.5 miles

15 minutes

3. Marcello is tiling his kitchen floor with

45 square tiles. The tiles come in whole-number side lengths of 6 to 12 inches. The function A(s) = 45s2, where s is the

side length of the tile, represents the area that Marcello can cover with the tiles. What is the domain of this function?

All real numbers between 6 and 12,

inclusive

All rational numbers between 6 and

12, inclusive

{6, 7, 8, 9, 10, 11, 12}

{6, 12}


4. Which values are in the domain of the

function f(x) = −6x + 11 with a range {−37, −25, −13, −1}?

1

2

3

4

5

6

7

8


5. The production cost for g graphing

calculators is C(g) = 25g. Evaluate the function at g = 15. What does the value of

the function at g = 15 represent?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. The domain of the function f(x) = 13x − x2

is given as {−2, −1, 0, 1, 2}. What is the range? Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7. Victor needs to find the volume of cube-shaped containers with side lengths

ranging from 2 feet to 7 feet. The side lengths of the containers can only be whole numbers. The volume of a container with side length s is given by

V(s) = s3.

a. What is the domain of the function?

________________________________________

________________________________________

b. Evaluate the function at each value in

the domain. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

8. A store selling televisions is calculating

the profit for one model. Currently, the store has 25 televisions in stock. The store bought these televisions from a

supplier for $99.50 each. Each television will be sold for $149.99.

a. Write a profit function in terms of n,

the number of televisions sold.

________________________________________

b. What is the domain of the function?

Explain.

________________________________________

________________________________________

________________________________________

________________________________________

c. If the store sold all of the televisions in stock, how much would the

profit be?

________________________________________

9. Tanya is printing a report. There are 100 sheets of paper in the printer, and

the number of sheets p left after t minutes of printing is given by the function p(t) = −8t + 100.

a. How long would it take the printer to

use all 100 sheets of paper? Explain

how you found your answer.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. What is the domain of the function?

Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. What is the range of the function?

Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

d. Tanya’s report takes 7 minutes to

print. How long is Tanya’s report? Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.3


1. Which function below generates the

sequence −2, 0, 2, 4, 6, …?

f(n) = n − 2, where n ≥ 0 and n is an

integer.

f(n) = 2n − 2, where n ≥ 0 and n is

an integer.

f(n) = −2n + 2, where n ≥ 1 and n is

an integer.

f(n) = 2n, where n ≥ 0 and n is an

integer.

2. The sequence −1, 2, 7, 14, … can be

generated by the function f(n) = n2 − 2. What is the domain of the function?

The domain is the set of all positive

real numbers.

The domain is the set of all real

numbers greater than 1.

The domain is the set of integers n

such that n ≥ 0.

The domain is the set of integers n

such that n ≥ 1.


3. Which of the functions below could be

used to generate the sequence 1, 2, 4, 8, 16, 32, …?


integer.


integer.

f(1) = 1, f(n) = 2(f(n − 1)), where n ≥ 2

and n is an integer.

f(n) = 2(n − 1), where n ≥ 1 and n is an integer.

f(n) = n2, where n ≥ 1 and n is an

integer.

Match each sequence with a function that generates it.

____ 4. 4, 12, 24, 40, 60,… A f(n) = 3n, n ≥ 1 and n is an integer.

____ 5.

0, 1

2, 23

, 34

, 45

, B f(n) = 2n(n + 1), n ≥ 1 and n is an integer.

____ 6. 48, 24, 12, 6, 3, … C f(n) = 2(n + 2), n ≥ 0 and n is an integer.

____ 7. 3, 6, 9, 12, 15, … D f (n) = n −1

n, n ≥ 1 and n is an integer.

____ 8. 3, 6, 11, 18, 27, … E f(n) = n2 + 2, n ≥ 1 and n is an integer.

F f(1) = 48 and f (n) = 1

2f (n −1) , n ≥ 2 and n is an integer.

G f(1) = 48 and f(n) = 2f(n − 1), n ≥ 2 and n is an integer.

H f (n) = n

n +1, n ≥ 1 and n is an integer.

Name ________________________________________ Date ___________________ Class __________________




9. Consider the sequence 1, 2, 5, 10, 17,

a. Write a quadratic function f(n) that

generates the sequence. Assume that the domain of the function is the set of integers n ≥ 0.

________________________________________

b. Use your result from part a to

determine the 15th term of the sequence.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

10. The domain of a function f defining the

sequence 23

, 34

, 45

, 56

, 67

, is the set of

consecutive integers starting with 1.

a. What is f(3)? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. How does your answer to part a

change if the domain of the function is the set of consecutive integers starting with 0?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

11. The Fibonacci sequence is

1, 1, 2, 3, 5, 8, 13, 21, …

a. Write a recursive function to describe

the terms of the Fibonacci sequence.

Begin with the conditions f(0) = f(1) = 1 and f(2) = f(1) + f(0).

________________________________________

________________________________________

b. Suppose the first two terms of the

Fibonacci sequence were f(0) = 2 and f(1) = 2, instead of f(0) = 1 and f(1) = 1. Write the first 5 terms of the

sequence.

________________________________________

________________________________________

c. Explain how you can modify your

answer from part a to describe the terms of the sequence found in part b.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

12. Consider the sequence 1, 3, 5, 7, 9, …

a. Write a function describing the sequence whose domain is the set of

consecutive integers starting with 1.

________________________________________

b. Write a recursive function describing

the sequence.

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.4*


1. The graph shows the height h(t) of a

model rocket t seconds after it is

launched from the ground at 48 feet per second. Where is the height of the rocket increasing? Where is it decreasing?

The height of the rocket is always

increasing.

The height of the rocket is always

decreasing.

The height of the rocket is increasing

when 0 < t < 3 and decreasing when

3 < t < 6.

The height of the rocket is increasing

when 3 < t < 6 and decreasing when 0 < t < 3.


2. Choose all the statements that are true

about the graph.

The x-intercept is 9.

The y-intercept is −2.

f(x) is increasing when x < 1.

f(x) is decreasing when x > 1.

f(x) has a local maximum at (1, −2).

f(x) has a local minimum at (1, −2).

f(x) is negative when x < 9.

f(x) is positive when x > −2.


3. Martha’s text message plan costs $15.00 for the

first 1000 text messages sent plus $0.25 per text over 1000 sent. Let C(t) represent the cost of sending t text messages over 1000. Sketch a

graph of this relationship, and find and interpret the C(t) -intercept.

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



4. The profit produced by an apple orchard increases as more trees are planted.

However, if the orchard becomes overcrowded, the trees will start to produce fewer apples, and the profit will start to decrease. The owner of a small

apple orchard recorded the following approximate profit values P(a) in the table below, where a is the number of apple trees in the orchard. Using the data in the

table, identify where P(a) is increasing and decreasing. Find when the owner earned the least profit and when the owner earned the most profit.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

5. The absolute value function y = |x| can be described using the following piecewise

function.

f (x) = −x, x < 0

x, 0 ≤ x⎧⎨⎩

a. Graph f(x).

b. Where is the function decreasing and

increasing?

________________________________________

________________________________________

________________________________________

________________________________________

c. Where is f(x) positive?

________________________________________

________________________________________

________________________________________

d. Explain why f(x) is never negative.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

a P(a) 0 0

10 1410

20 2380

30 3010

40 3220

50 3050

60 2400

70 1420

80 0

Name ________________________________________ Date ___________________ Class __________________



F.IF.5*


1. The function h(n) gives the number of

person-hours it takes to assemble n

engines in a factory. What is a reasonable domain for h(n)?

The nonnegative rational numbers

The real numbers

The nonnegative integers

The nonnegative real numbers

2. The graph of the quadratic function f(x) is shown below. What is the domain of f(x)?

The integers greater than −3.

The real numbers greater than −3.

The integers

The real numbers

3. The growth of a population of bacteria

can be modeled by an exponential

function. The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks, that has passed. The initial population of the

bacteria colony was 500. What is the domain of the function? What does the domain represent in this context?

The domain is the real numbers

greater than 500. The domain represents the time, in weeks, that has passed.

The domain is the real numbers

greater than 500. The domain represents the population of the colony after a given number of weeks.

The domain is the nonnegative real numbers. The domain represents the

time, in weeks, that has passed.

The domain is the nonnegative real

numbers. The domain represents the population of the colony after a given number of weeks.

Name ________________________________________ Date ___________________ Class __________________




4. The function h(t) describes the height, in

feet, of an object at time t, in seconds, when it is launched upward from the ground at an initial speed of 112 feet

per second.

a. Find the domain.

________________________________________

b. What does the domain mean in this context?

________________________________________

________________________________________

5. What are the domain and range of the

exponential function f(x)?

________________________________________

________________________________________

6. An electronics store sells a certain brand

of tablet computer for $500. To stock the tablet computers, the store pays $150 per

unit. The store also spends $1800 setting up a special display area to promote the product.

a. Write a function rule to describe the

profit earned from selling the tablet

computers. Note that profit is the revenue earned minus the cost.

________________________________________

b. What is a reasonable domain for the

function? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

c. What are the first eight values in the

range of the function? (Start with the range value that corresponds to the

least value in the domain.)

________________________________________

________________________________________

________________________________________

7. A grocery store sells two brands of ham

by the pound. Brand A costs $4.19 per pound, and brand B costs $4.79 per pound. Brand A can be purchased at the

deli in any amount, whereas brand B comes in prepackaged containers of either 0.5 pound or 1 pound. Write a function rule that represents the revenue

earned for each of the brands and determine a reasonable domain for each. Explain your answers.

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.6*


1. The table shows the height of a sassafras

tree at each of two ages. What was the

tree’s average rate of growth during this time period?

Age (years) Height (meters)

4 2

10 5

0.4 meter per year

0.5 meter per year

2 meters per year

2.5 meters per year

2. The graph shows the height h, in feet, of

a football at time t, in seconds, from the moment it was kicked at ground level.

Estimate the average rate of change in height from t = 1.5 seconds to t = 1.75 seconds.

−20 feet per second

−12 feet per second

12 feet per second

20 feet per second

3. Find the average rate of change of the

function f (x) = 2 x − 5 + 3 from x = 9 to

x = 21.

−3 13

− 1

3 3


4. A person’s body mass index (BMI) is

calculated by dividing the person’s mass

in kilograms by the person’s height in meters. The table shows the median BMI for U.S. males from age 2 to age 12. For which intervals is the average rate of

change in the BMI positive?

age 2 to age 4

age 4 to age 6

age 6 to age 8

age 8 to age 10

age 10 to age 12

Select the correct answer for each

lettered part.

5. Determine whether each function’s

average rate of change on the interval x = 0 to x = 2 is equal to 2.

a. f(x) = x + 2 Yes No

b. f(x) = 2x Yes No

c. f (x) = x

2 Yes No

d. f(x) = x2 Yes No

e. f(x) = 2x Yes No

Age (years) Median BMI

2 16.575

4 15.641

6 15.367

8 15.769

10 16.625

12 17.788

Name ________________________________________ Date ___________________ Class __________________




6. The table gives the minutes of daylight on

the first and last day of October 2012 for Anchorage, Alaska, and Los Angeles, California.

Location Daylight on Oct. 1

Daylight on Oct. 31

Anchorage 686 517

Los Angeles 711 650

a. Calculate the average rate of

change, in minutes per day, of daylight during October for each location.

________________________________________

________________________________________

b. Interpret your answers from part a. In other words, how are the day lengths

changing in Anchorage and Los Angeles in October?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. The sun rises at 7:00 A.M. on

October 17, 2012, in Los Angeles. Estimate the time at which the sun

sets that day. Explain your reasoning and show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

7. The graph models the population P(t) of a bacteria colony as a function of time t, in weeks.

a. Determine the average growth rate

between weeks 2 and 3.

________________________________________

b. Determine the average growth rate


________________________________________

c. Determine the average growth rate


________________________________________

d. What is happening to the average

growth rate as each week passes? Justify your answer.

________________________________________

________________________________________

________________________________________

________________________________________

e. What do you think the average growth rate will be between weeks

5 and 6 if the pattern continues?

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.7a*


1. What are the intercepts of the linear function shown?

x-intercept: −2; y-intercept: −2 x-intercept: −2; y-intercept: 4

x-intercept: 2; y-intercept: 4

x-intercept: 2; y-intercept: −4

2. What is the vertex of the quadratic function f(x)? Is it a maximum or a minimum?

(1, −4); minimum

(0, −3); minimum

(−1, 0); minimum

(3, 0); maximum


3. Sally decides to make and sell necklaces to earn money to buy a new computer. She plans to charge $5.25 per necklace. a. Write a function that describes the

revenue R(n), in dollars, Sally will earn from selling n necklaces.

________________________________________

b. What is a reasonable domain for this function?

________________________________________

________________________________________

________________________________________

c. Graph the function.

d. Identify and interpret the intercepts of

the function.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



4. The function h(t) = −4.9t2 + 24.5t models

the height h(t), in meters, of an object t seconds after it is thrown upward from

the ground with an initial velocity of 24.5 meters per second.

a. Calculate and interpret the intercepts

of the function.

________________________________________

________________________________________

________________________________________

________________________________________

b. Calculate the vertex of the function.

________________________________________

________________________________________

________________________________________

________________________________________

c. Is the vertex a minimum or a

maximum? What does this mean in this context?

________________________________________

________________________________________

________________________________________

________________________________________

d. Plot the points found in parts a and b

and then graph the function.

5. A farmer has 1200 feet of fencing to

enclose a square area for his horses and a rectangular area for his pigs. The

farmer decides that the enclosures should share a full side to maximize the usefulness of the fencing. He also wants to maximize the combined area of the

enclosures. Write a function that describes the combined area of the enclosures A(s) as a function of the side length s of the square enclosure. Then,

graph the function to determine dimensions of each enclosure that maximize the combined area. Explain your answer.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.7b*


1. What kind of function best describes the following graph?

An absolute value function

A cube root function

A square root function

A step function

2. What are the x- and y-intercept(s) of f(x)?

x-intercept: 1

y-intercept: −1

x-intercept: −5; y-intercept: −1

x-intercepts: −5, 1; y-intercept: −1

3. What is the vertex of f(x)? Is it a maximum or a minimum?

(0, −2); minimum

(3, −5); minimum

(−2, 0); minimum

(8, 0); maximum


4. Graph the piecewise defined function. What are the domain and range?

f (x) =

−2 x < −31 −3 ≤ x <14 x ≥1

⎧⎨⎪

⎩⎪

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. A simple reaction time test involves dropping a meter-long ruler between

someone’s thumb and index finger and measuring the time it takes for the person to catch it against the distance the ruler

travels. The function t(d) = 0.045 d

models the approximate reaction time t(d), in seconds, as a function of the distance d the ruler travels, in

centimeters. Graph the function. What happens to the reaction time as the distance increases? Explain your answer by interpreting the graph.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. Write and graph a piecewise-defined step function f(x) that has the following

characteristics.

I. f(x) has more than one x-intercept

II. The domain of f(x) is the real

numbers

III. The range of f(x) consists of

four unique integers

________________________________________

7. Graph the function f (x) = 2 x − 63 + 4

Find the intervals where the function is increasing and decreasing.

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.7e*


1. The exponential function f(x) has a

horizontal asymptote at y = 3. What is the

end behavior of f(x)?

As x decreases without bound, f(x) decreases without bound. As x increases without bound, f(x) increases without bound.

As x decreases without bound, f(x) increases without bound. As x increases without bound, f(x) decreases without bound.

As x decreases without bound, f(x) approaches, but never reaches, 3. As x increases without bound, f(x) increases without bound.

As x decreases without bound, f(x) decreases without bound. As x increases without bound, f(x) approaches, but never reaches, 4.

2. A website allows its users to submit and

edit content in an online encyclopedia.

The graph shows the number of articles a(t) in the encyclopedia t months after the website goes live. How many articles were in the encyclopedia when it

went live?

0 60

30 180


3. Which statements are true about the graph of the exponential function f(x)?

The domain is all real numbers.

The range is all real numbers.

The f(x)-intercept is 3.

The x-intercept is −1.

As x increases without bound, f(x) approaches, but never reaches, −1.

Name ________________________________________ Date ___________________ Class __________________




4. Suppose an exponential function has a

domain of all real numbers and a range that is bounded by an integer. How many x-intercepts could such a function have?

Graph examples to support your answer.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

5. The value of an object decreases from its

purchase price over time. This change in value can be modeled using an

exponential function. A new copy machine purchased by a school for $1200 has an estimated useful life span of 12 years. After 12 years, the copier is

worth $250. The value V(t) of the copier after t years is approximated by the function V(t) = 1200(0.88)t.

a. Graph the function on the domain

0 ≤ t ≤ 12.

b. Estimate and interpret the

V(t)-intercept.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.8a


1. What are the zeros of the function

f(x) = x2 + 2x − 8?

x = 4 and x = −2

x = −4 and x = 2

x = −4 and x = −2

x = 4 and x = 2

2. What is the axis of symmetry of the graph

of f(x) = 3x2 − 6x + 6?

x = −1

x = 1

y = 1

y = 3


3. Which of the following statements

correctly describe the graph of f(x) = 2x2 + 8x − 2?

The maximum value of the function

is 10.

The minimum value of the function

is −10.

The axis of symmetry is the line

x = −2.

The axis of symmetry is the line x = 2.

The graph is a parabola that

opens up.

The graph is a parabola that

opens down.

Select the correct answer for each lettered part.

4. Consider the function f(x) = 2x2 + 4x − 30. Classify each statement.

a. The vertex of the graph of f(x) is (1, −32). True False

b. The zeros of f(x) are x = 3 and x = −5. True False

c. The graph of f(x) opens down. True False

d. The axis of symmetry is x = −1. True False

e. The y-intercept of f(x) is −30. True False


5. Consider the function f(x) = 4x2 + 4x − 15.

a. Factor the expression 4x2 + 4x − 15. What are the zeros of f(x)?

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

b. What are the coordinates of the vertex of f(x)? Is the vertex the maximum or minimum

value of the function? Explain.

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. The axis of symmetry for a quadratic function is a vertical line halfway between the x-intercepts of the function. Miguel says that the graph of

f(x) = −2x2 − 16x − 34 has no axis of symmetry because the function has no x-intercepts.

a. Explain why Miguel is incorrect.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Find the axis of symmetry of the

graph of f(x). Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

7. The arch that supports a bridge that

passes over a river forms a parabola whose height above the water level is

given by h(x) = − 9

125x2 + 45, where x = 0

represents the center of the bridge. The

distance between the sides of the arch at the water level is the same as the length of the bridge.

a. How long is the bridge? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. A sailboat with a mast that

extends 50 feet above the water is

sailing down the river. Will the sailboat be able to pass under the bridge? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.8b


1. The balance B, in dollars, after t years of

an investment that earns interest

compounded annually is given by the function B(t) = 1500(1.045)t. To the nearest hundredth of a percent, what is the monthly interest rate for

the investment?

0.37% 4.50%

3.67% 69.59%

2. After t days, the mass m, in grams, of

100 grams of a certain radioactive element is given by the function m(t) = 100(0.97)t. To the nearest percent, what is the weekly decay rate of the

element?

3% 21%

19% 81%


3. Which of these functions describe

exponential growth?

f(t) = 1.25t

f(t) = 2(0.93)0.5t

f(t) = 3(1.07)3t

f(t) = 18(0.85)t

f(t) = 0.5(1.05)t

f(t) = 3(1.71)5t

f(t) = 0.682t

f(t) = 8(1.56)1.4t


4. Determine if each function below is equivalent to f(t) = 0.25t.

a. f (t) = 1t4 Equivalent Not equivalent

b. f (t) = 0.522t Equivalent Not equivalent

c. f (t) = 0.0625t2 Equivalent Not equivalent

d. f (t) = 0.125t2 Equivalent Not equivalent

e. f (t) = 4−t Equivalent Not equivalent

f. f (t) = -0.25−t Equivalent Not equivalent


5. The population P, in millions, of a certain country can be modeled by the function

P(t) = 3.98(1.02)t, where t is the number of years after 1990. a. Write the equation in the form P(t) = a(1 + r)t.

_________________________________________________________________________________________

b. What is the value of r in your answer from part a? What does this value represent?

_________________________________________________________________________________________

_________________________________________________________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. How do the function values of

g(x) = 200(4x − 1) compare to the corresponding function values of

f(x) = 200(4x)? Explain using a transformation of g(x).

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

7. The value V, in dollars, after t years of an

investment that earns interest compounded annually is given by the

function V(t) = 1500(1.035)t.

a. Rewrite V(t) to find the annual

interest rate of the investment.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Find the approximate interest rate

over a 5-year period by rewriting the function using the power of a power property. Round to the

nearest percent.

________________________________________

________________________________________

________________________________________

8. Sanjay plans to deposit $850 in a bank account whose balance B, in dollars, after

t years is modeled by B(t) = 850(1.04)t.

a. Write the equation in the form

B(t) = a(1 + r)t. What is the annual interest rate of Sanjay’s account?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Rewrite the equation from part a to

approximate the monthly interest

rate. Round to the nearest hundredth of a percent.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. Rebecca deposits $850 in a bank

account that earns 0.35% interest compounded monthly. Without calculating the account balances,

which account will have a larger balance after 6 months? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.IF.9


1. A quadratic function is shown below.

Which function has the same domain?

f (x) = x − 2

g(x) = x − 2

h(x) = x − 2

k(x) = 3x, x ≥ −2

2. The function f(x) is defined for only the values given in the table. Which function

has the same x-intercepts as f(x)?

x f(x) −2 2.5

−1 0

0 −1.5 1 −2 2 −1.5 3 0 4 2.5

g(x) = 2x + 2

h(x) = − 1

3x + 2

j(x) = x2 + 2x − 3

k(x) = |x − 1| − 2


3. Which functions have the same range

as the cube root function f(x) shown in the graph?

g(x) = x + 2

h(x) = 1

3x +1

j(x) = x2 − 6x + 8

k(x) = − | 2x | −1

m(x) = 2x −13 + 2


4. The function f(x) is defined for only the

values in the table. Let g(x) = x2 + 3 for all real numbers 1 ≤ x ≤ 4. Compare the domains, ranges, and initial values of

the functions.

x f(x) 1 4 2 6 3 10 4 18

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. Which of the functions described below

has a greater maximum value on the domain −6 ≤ x ≤ 6? Explain.

x g(x) x g(x) −6 −13 1 4.5

−5 −7.5 2 3

−4 −3 3 0.5

−3 0.5 4 −3

−2 3 5 −7.5

−1 4.5 6 −13 0 5

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. A company offers two cell phone plans to

its employees. The function A(t) = 70t gives the cost, in dollars, of cell phone

plan A for t months. Plan B allows an employee to receive an additional discount by paying for a certain number of months in advance. The table

describes the function B(t), which gives the cost, in dollars, of cell phone plan B for t months.

t B(t) 1 $70 2 $140 3 $200 4 $250 5 $290 6 $330

a. Which plan costs more for

3 months? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. After how many months will an

employee on plan B be saving more

than $50 over an employee on plan A? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.BF.1a*


1. A small swimming pool initially contains

400 gallons of water, and water is being

added at a rate of 10 gallons per minute. Which expression represents the volume of the pool after t minutes?

−10t + 400

10t + 400

400t + 10

400(1.10)t

2. A diver jumps off a 10-meter-high diving

board with an initial vertical velocity of 3 meters per second. The function h(t) = −4.9t2 + v0t + h0 models the height

of a falling object, where v0 is the initial vertical velocity and h0 is the initial height. Which function models the divers height h, in meters, above the water at time t, in

seconds?

h(t) = −4.9t2 − 3t + 10

h(t) = −4.9t2 − 3t − 10

h(t) = −4.9t2 + 3t + 10

h(t) = −4.9t2 + 3t − 10

3. Andrea buys a car for $16,000. The car

loses value at a rate of 8% each year. Which recursive rule below describes the value of Andrea’s car V, in dollars, after t years?

V(0) = $16,000 and V(t) = 0.08 i V(t − 1) for t ≥ 1

V(0) = $16,000 and

V(t) = 0.2 i V(t − 1) for t ≥ 1

V(0) = $16,000 and

V(t) = 0.92 i V(t − 1) for t ≥ 1

V(0) = $16,000 and

V(t) = 1.08 i V(t − 1) for t ≥ 1


4. Miguel has $250 dollars saved, and he

adds $5 to his savings every week. Which functions describe the amount A, in dollars, that Miguel has saved after t weeks?

A(t) = 5t + 250

A(t) = −5t + 250

A(t) = 250t + 5

A(0) = 250 and A(t) = A(t − 1) + 5 for

t ≥ 1

A(0) = 250 and A(t + 1) = A(t) + 5 for

t ≥ 0

A(0) = 250 and A(t + 1) = 5A(t) for

t ≥ 0


5. When a piece of paper is folded in half,

the total thickness doubles and the total area is halved. Suppose you have a sheet of paper that is 0.1 mm thick and has an area of 10,000 mm2.

a. Write an equation that models the thickness T, in millimeters, of the

sheet of paper after it has been folded n times.

________________________________________

________________________________________

________________________________________

________________________________________

b. Write an equation that models the

area A, in square millimeters, of the sheet of paper after it has been

folded n times.

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. The people at a conference use the

following exercise to get to know each other. The leader of the conference

chooses 4 people, greets each of them with a handshake, and they chat. After one minute, those 4 people each choose 4 people, greet each with a handshake,

and chat. This continues until each person at the conference has shaken someone’s hand. Write an exponential function that models the number of

handshakes H in the nth minute.

________________________________________

7. A population of 300 sea turtles grows by

5% each year.

a. Describe the steps needed to

calculate the population each year.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Write a recursive function for the

population P after t years.

________________________________________

________________________________________

8. Simon wants to use 500 feet of fencing to

enclose a rectangular area in his backyard.

a. Write a function for the enclosed area

A, in square feet, in terms of the width w, in feet. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. What are the dimensions of the

largest rectangle Simon can enclose with 500 feet of fencing? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.BF.1b*


1. A rectangle has side lengths (x + 4) feet

and (2x + 1) feet for x > 0. Write a

function that describes the area A, in square feet, in terms of x.

A(x) = 3x + 5

A(x) = 6x + 10

A(x) = 2x2 + 9x + 4

A(x) = 2x2 + 7x − 4

2. In a factory, the cost of producing n items

is C(n) = 25n + 150. Which function describes the average cost of producing one item when n items are produced?

A n( ) = 25n +150

A(n) = 25 + 150

n

A n( ) = 25n2 +150n

A(n) = 25

n+ 150

n2


3. Two identical water tanks each hold

10,000 liters. Tank A starts full, but water is leaking out at a rate of 10 liters per minute. Tank B starts empty and is filled at a rate of 13 liters per minute. Which

functions correctly describe the combined volume V of both tanks after t minutes?

V(t) = 10,000 − 10t + 13t

V(t) = 10,000 − 10t − 13t

V(t) = 10,000 + 10t − 13t

V(t) = 10,000 − 3t

V(t) = 10,000 + 3t

V(t) = 10,000 − 23t


4. Let f(x) = x2 − x − 2 and g(x) = x2 + x − 6. Classify each function below as linear, quadratic,

or neither.

a. f(x) + g(x) Linear Quadratic Neither

b. f(x) − g(x) Linear Quadratic Neither

c.

f (x)g(x)

Linear Quadratic Neither

d. f(x) i g(x) Linear Quadratic Neither


5. Let f(x) = x2 + x − 6 and g(x) = x2 − 4. Find f(x) + g(x) and f(x) − g(x). Simplify your answers.

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. Esther exercises for 45 minutes. She rides her bike at 880 feet per minute for

t minutes and then jogs at 400 feet per minute for the rest of the time.

a. Write a function that describes the

distance d1, in feet, that Esther travels while riding her bike for

t minutes.

________________________________________

b. Write a function that describes the

distance d2, in feet, that Esther travels while jogging.

________________________________________

c. Use your answers from parts a and b

to write a function that describes the distance d, in feet, that Esther travels

while exercising.

________________________________________

________________________________________

7. Trina deposits $1500 in an account that

earns 5% interest compounded annually. Pablo deposits $1800 in an account that earns 2.5% interest compounded

annually. Write a function that models the difference D, in dollars, between the balance of Trina’s account and the balance of Pablo’s account after t years.

(Hint: The difference between the two balances should always be positive.)

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

8. Town A and town B both had a population of 15,000 people in the year

2000. The population of town A increased by 2.5% each year. The population of town B decreased by 3.5% each year.

a. Write a function A(t), the population

of town A t years after 2000.

________________________________________

b. Write a function for B(t), the

population of town B t years after 2000.

________________________________________

c. Find A(t) + B(t) and

A(t)B(t)

. Simplify

your answers and interpret each function in terms of the situation.

If necessary, round decimals to the nearest thousandth.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.BF.2*


1. A theater has 18 rows of seats. There are

22 seats in the first row, 26 seats in the

second row, 30 seats in the third row, and so on. Which of the following is a recursive formula for the arithmetic sequence that represents this situation?

f(0) = 18, f(n) = f(n − 1) + 4

for 1 ≤ n ≤ 18

f(1) = 22, f(n) = f(n − 1) + 4

for 2 ≤ n ≤ 18

f(n) = 18 + 4n

f(n) = 22 + 4(n − 1)

2. The table below shows the balance b, in

dollars, of Daryl’s savings account t years after he made an initial deposit. What is an explicit formula for the geometric sequence that represents this situation?

b(t) = 1.015(1218)t − 1

b(t) = 1218(1.015)t

b(t) = 1218 + 1.015(t − 1)

b(t) = 1218(1.015)t − 1


3. Amelia earns $36,000 in the first year

from her new job and earns a 6% raise each year. Which of the following models Amelia’s pay p, in dollars, in year t of her job?

p(0) = 36,000, p(t) = 1.06 i p(t − 1)

for t ≥ 1

p(1) = 36,000, p(t) = 1.06 i p(t − 1)

for t ≥ 2

p(t) = 36,000 i 1.06t − 1 for t ≥ 1

p(t) = 1.06 i 36,000t − 1 for t ≥ 1

p(t) = 1.06(t − 1) + 36,000 for t ≥ 1

p(t) = 38,160 i 1.06t − 2 for t ≥ 1


4. Calvin is practicing the trumpet for an

audition to play in a band. He starts practicing the trumpet 40 minutes the first

day and then increases his practice time by 5 minutes per day. The audition is on the 10th day.

a. Write a recursive rule that represents

the time t, in minutes, Calvin

practices on day d.

________________________________________

________________________________________

b. Write an explicit rule that represents

the time t, in minutes, Calvin practices on day d.

________________________________________

________________________________________

c. Use the result from part b to find how

long Calvin practices on the 8th day. Show your work.

________________________________________

________________________________________

________________________________________

Time, t (years)

Balance, b (dollars)

1 $1218

2 $1236.27

3 $1254.81

4 $1273.64

Name ________________________________________ Date ___________________ Class __________________



5. The table displays the speed of a car s, in feet per second, t seconds after it starts coasting.

a. Explain why this sequence

is geometric.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Write an explicit rule for this

sequence using the values from the table.

________________________________________

________________________________________

c. Use the result from part b to write a

recursive rule for this sequence.

________________________________________

________________________________________

d. What is the speed of the car when it

begins to coast? Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. The table below shows the cost c, in

dollars, of a private party on a boat based on the number of people p attending.

a. Does an arithmetic sequence or a

geometric sequence model this situation? Justify your answer by

using the values in the table.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Write an explicit formula and a

recursive formula for the sequence. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

c. How much would it cost for 44 people

to attend the private party? Show

your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Time, t (seconds)

Speed, s (ft/sec)

1 57 2 54.15 3 51.44 4 48.87

People, p Cost, c (dollars)

2 306 3 334 4 362 5 390

Name ________________________________________ Date ___________________ Class __________________



F.BF.3


1. The graph of g(x) is shown below. The

graph of g(x) can be obtained by applying

horizontal and vertical shifts to the parent

function f (x) = x3 . What is g(x)?

g(x) = x − 23 + 4

g(x) = x + 23 − 4

g(x) = x + 43 − 2

g(x) = x − 43 + 2

2. What must be done to the graph of

f(x) = |x| to obtain the graph of the function g(x) = 0.5|x + 4| − 10?

The graph of f(x) is shifted left

4 units, horizontally shrunk by a factor of 0.5, and shifted down

10 units.

The graph of f(x) is shifted right

4 units, vertically shrunk by a factor of 0.5, and shifted down 10 units.


4 units, vertically shrunk by a factor

of 0.5, and shifted down 10 units.


4 units, vertically shrunk by a factor of 0.5, and shifted up 10 units.


3. Describe the transformations applied to

the graph of the parent function f (x) = x

used to graph g(x) = −2 1− x + 3. Graph

g(x).

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

4. Describe how the nonzero slope m of a

linear function g(x) = mx is a transformation of the graph of the parent linear function f(x) = x.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. For the following graphs of transformed functions, state the parent function f(x), the type of transformation, and write a function rule. a.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b.

________________________________________

________________________________________

________________________________________

________________________________________

6. a. Rewrite g(x) = − 1

2x2 − 2x + 2 in

vertex form. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Describe the transformations applied to the parent function f(x) = x2.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. Graph g(x).

Name ________________________________________ Date ___________________ Class __________________



F.BF.4a


1. What is the inverse of f(x) = −2x + 6?

g(x) = 1

2x − 3

g(x) = −

12

x + 3

g(x) = 2x − 6

g(x) = −

12

x + 6

2. The point (2, 12) is on the graph of f(x).

Which of the following points must be on the graph of g(x), the inverse of f(x)?

(−2, 12)

(2, −12)

(2, 12)

(12, 2)


3. If f (x) = −

18

x + 5, which of the following

statements about g(x), the inverse of f(x), are true?

g(−2.125) = 57

g(−0.5) = 44

g(−0.375) = 37

g(0.125) = 39

g(0.625) = 45

g(1.125) = 40


4. Let f(x) = −13x + 52. Find the inverse of

f(x) and use it to find a value of x such that f(x) = 182. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

5. At a carnival, you pay $15 for admission,

plus $3 for each ride you go on.

a. Write a function A(r) that models the

amount A, in dollars, you would spend to ride r rides at the carnival.

________________________________________

b. Find the inverse of A(r). Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. What does the inverse function found

in part b represent in the context of

the problem?

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. The graph of f(x) = 3x − 6 is shown, along with the dashed line y = x.

a. Find g(x), the inverse of f(x). Show

your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Graph g(x) on the coordinate grid above.

c. How are the graphs of f(x) and g(x) related to the line y = x?

________________________________________

________________________________________

________________________________________

7. a. Find g(x), the inverse of f(x) = mx + b. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

b. Use the formula for g(x) to find the

inverse of f(x) = 4x + 11.

________________________________________

c. Does every linear function have an

inverse? Use your result from part a to explain why or why not. If not, give the general forms of any linear

functions that do not.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.LE.1a*


1. For some exponential function f(x),

f(0) = 12, f(1) = 18, and f(2) = 27. How

does f(x) change when x increases by 1?

f(x) grows by a factor of 23

.

f(x) grows by a factor of 32

.

f(x) increases by 6.

f(x) increases by 9.

2. The balance B of an account earning

simple interest is $1000 when the account is opened, $1075 after one year, and $1150 after two years. How does the balance of the account change from one

year to the next?

The balance increases by 7.5%.

The balance decreases by 7.5%.

The balance increases by $75.

The balance increases by $150.


3. Marco starts reading a 350-page book at

9 a.m. The number of pages P Marco has left to read t hours after 9 a.m. is modeled by the function P(t) = 350 − 45t. During which of the following time periods does

Marco read the same number of pages he reads between 11 a.m. and 1 p.m.?

9 a.m. to 11 a.m.

11 a.m. to 12 noon

12:30 p.m. to 1:30 p.m.

2 p.m. to 4 p.m.

1:30 p.m. to 3.30 p.m.

Match each statement in the proof with the correct reason below.

Given: x2 − x1 = x4 − x3, f(x) = abx

Prove:

f (x2)f (x1)

=f (x4)f (x3)

____ 4. x2 − x1 = x4 − x3, f(x) = abx

____ 5. bx2−x1 = bx4−x3

____ 6.

bx2

bx1= bx4

bx3

____ 7.

abx2

abx1= abx4

abx3

____ 8.

f (x2)f (x1)

=f (x4)f (x3)

A Given

B Power of powers property

C Distributive property

D Subtraction property of equality

E Definition of f(x)

F Quotient of powers property

G If x = y, then bx = by

H Multiplication property of equality

Name ________________________________________ Date ___________________ Class __________________




9. Complete the reasoning to prove that linear functions grow by equal differences

over equal intervals.

Given: x2 − x1 = x4 − x3

f(x) is a linear function of the form f(x) = mx + b.

Prove: f(x2) − f(x1) = f(x4) − f(x3)

x2 − x1 = x4 − x3 Givenm(x2 − x1) = m(x4 − x3) ____________mx2 −mx1 = mx4 −mx3 ____________

mx2 + b −mx1 − b = mx4 + ___−mx3 − ___ Addition and subtraction properties(mx2 + b)− (mx1 + b) = ________________ Distributive property

f (x2)− f (x1) = ___________ Definition of f (x)

10. Sandra’s annual salary S, in dollars, after

working at the same company for t years is given by the function S(t) = 38,000 + 1500t. a. Complete the table showing

Sandra’s salary after each year for the first five years.

b. Show that Sandra’s salary increases by the same amount each year.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

11. The population of a certain town is

3500 people in 2000. The population of the town P is modeled by the function P(t) = 3500(0.97)t, where t is the number

of years after 2000.

a. By what factor did the population

change between 2000 and 2001? Between 2001 and 2002? Round your answers to the nearest

hundredth. Show your work. What do you notice?

________________________________________

________________________________________

________________________________________

________________________________________

b. By what factor did the population

change between 2000 and 2002? Between 2001 and 2003? Round your answers to the nearest

hundredth. Show your work. What do you notice?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Time, t (years)

Salary, S (dollars)

1 2 3 4 5

Name ________________________________________ Date ___________________ Class __________________



F.LE.1b*


1. In which of the following situations does

Michael’s salary change at a constant

rate relative to the year?

Michael’s starting salary is $9500

and increases by 4% each year.

Michael’s starting salary is $9500

and increases by $500 each year.

Michael’s starting salary is $9500.

He receives a $500 raise after one year and a $600 raise after the

second year.

Michael’s starting salary is $9500.

He receives a 4% raise after one year and a 5% raise after the second year.

2. The table shows the population of two cities. Which city’s population is changing

at a constant rate per year?

Year City A City B 2009 700,000 570,000 2010 697,500 580,000 2011 694,500 590,000 2012 690,500 600,000

A

B

Both A and B

Neither A nor B


3. Determine which situations describe an

amount of money changing at a constant rate relative to a unit change in time of the specified unit.

The value of David’s car decreases

by 11% each year.

Susan adds $50 to a savings

account each week.

The price of a stock each week is

105% of its price from the previous week.

Monica pays $700 for car insurance

the first year and pays an additional $10 per year.

The amount Ariel and Miguel pay to

rent a car for $40 a day.


4. For which of these functions does the

function value change at a constant rate per unit change in x? Explain.

x f(x) g(x) h(x) 1 6 1 31 2 12 2 25 3 20 4 19 4 30 8 13 5 42 16 7

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. Samantha started a new job, and is paid

$10.50 an hour. Each month, Samantha earns a $0.25 per hour raise. Does

Samantha’s hourly pay grow at a constant rate per unit change in month? Explain.

________________________________________

________________________________________

________________________________________

6. Alonzo and Katy hike 4 miles in 2 hours

and then break to eat lunch. After lunch,

they hike for 45 minutes and travel 1.5 miles. Not including the time spent eating lunch, do Alonzo and Katy hike at a constant rate? If not, explain why not.

If so, what is the unit rate?

________________________________________

________________________________________

________________________________________

________________________________________

7. Tim works as a salesperson for a

furniture store.

His first year, he earns a base pay of

$25,000 plus a 5% commission on every item he sells. His second year, he earns a base pay of $26,000 plus a

6.5% commission.

His third year, he earns a base pay of

$27,040 plus an 8% commission.

Decide if each of the quantities below

changes at a constant rate per unit change in year. Explain your answers.

a. Tim’s base pay.

________________________________________

________________________________________

b. Tim’s commission rate.

________________________________________

________________________________________

8. Companies A and B each employ 500 workers. Company A decides to

increase its workforce by 10% each year. Company B decides to increase its workforce by 50 workers each year.

a. Complete the table to show each

company’s workforce for the first

3 years after implementing the plan to increase its workforce. Round down to the nearest person.

Year Company A Company B 0 500 500 1 2 3

b. For each company, find the amount

by which the workforce changed each year. Which company’s workforce has a constant rate of growth per unit change of year?

Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

c. Use your results from part b to

determine that company’s workforce 4 years after implementing the plan to increase its workforce.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.LE.1c*


1. In which of the following situations does

Pam’s hourly wage change by a constant

percent per unit change in year?

Pam’s starting hourly wage is $14.50

per hour the first year, and it increases by $1.50 each year.

Pam’s starting hourly wage is

$13.00. She receives a $0.50 per hour raise after one year, a $0.75 per

hour raise after the second year, a $1.00 per hour raise after the third year, and so on.

Pam’s hourly wage is $20 per hour in

the first year, $22 per hour the

second year, $24.20 per hour the third year, and so on.

Pam’s starting hourly wage is $15.00.

Her hourly wage is $15.75 after one year, $17.00 after two years, $18.75

after three years, and so on.

2. The table shows the value, in dollars, of

three cars after they are purchased. Which car’s value decreases by a constant percent?

Year Car A Car B Car C 0 $21,000 $18,000 $25,000 1 $18,000 $15,625 $22,500 2 $15,000 $13,250 $20,250

Car A

Car B

Car C

Cars B and C


3. Which of the following situations describe

a quantity that increases by a constant percent that is at least 20% per unit time?

There are 400 bacteria in a Petri dish

the first day, 700 the second day, 1225 the third day, and so forth.

The number of fish in the lake is

24 the first year, 48 in the second

year, 72 in the third year, and so on.

The number of visitors for a website

is 4000 one month, 5200 the second month, 6760 the third month, and so on.

The price for a gallon of cooking oil is $3.00 the first year, $3.30 the second

year, $3.63 the third year, and so on.

The population of a town is

10,000 the first year, 11,500 the second year, 13,225 the third year, and so on.


4. For which of these functions does the

function value change at a constant factor

per unit change in x? Explain.

x f(x) g(x) h(x) 1 512 18 65 2 128 16 33 3 32 14 17 4 8 12 9 5 2 10 5

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



5. In one year, a population of endangered

turtles laid 8000 nests. Each year, the number of nests is half as many as the

number of nests in the previous year. Does the number of nests change by a constant percent per unit change in a year? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. The table shows the mass, in grams, of

the radioactive isotope carbon-11 after it starts decaying. Does the mass of the substance decay by a constant percent each minute? If so, find the decay rate.

Explain and round to the nearest hundredth of a percent. If not, explain why not.

Time (minutes)

Mass (grams)

0 500 1 483.24 2 467.05 3 451.40

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

7. Carol inherited three antiques one year.

The value, in dollars, of each antique for the first few years after she inherited the

antiques is shown in the table. Time

(years) Antique

toy Antique

vase Antique

chair

0 $70.00 $25.00 $100.00 1 $77.00 $30.00 $108.00 2 $84.70 $37.50 $116.64 3 $93.17 $47.50 $125.97

Which antiques have a value that grows

by a constant factor relative to time? Of those antiques, which antique increases its value at a faster rate? Explain your

answers.

________________________________________

________________________________________

________________________________________

8. Two competing companies redesigned

their websites during the same month. The table shows the number of visits each website receives per month after the redesigns. Jeff thinks that the number

of visits for both websites grows by a constant percent per month.

Month Company A

Company B

0 120,000 150,000 1 126,000 153,000 2 132,300 157,590 3 138,915 159,166

a. Is Jeff correct about company A?

Justify your answer.

________________________________________

________________________________________

________________________________________

b. Is Jeff correct about company B?

Justify your answer.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.LE.2*

SELECTED RESPONSE Select all correct answers.

1. Emile is saving money to buy a bicycle.

The amount he has saved is shown in the

table. Which of the functions below describe the amount A, in dollars, Emile has saved after t weeks?

A(t) = 15 + 15(t − 1)

A(t) = 30 + 15(t − 1)

A(t) = 15 + 15t

A(t) = 30 + 15t

A(t) = 30(1.5)t

A(t) = 15(2)t

Select the correct answer.

2. Which function models the relationship

between x and f(x) shown in the table?

f (x) = 1

2x f(x) = 2x − 3

f(x) = x − 1 f(x) = 4x − 7

3. Sasha invests $1000 that earns 8%

interest compounded annually. Which

function describes the value V of the investment after t years?

V(t) = 1000 + 80t

V(t) = 1000(0.08)t

V(t) = 1000(0.92)t

V(t) = 1000(1.08)t


4. A $100 amount is invested in two

accounts. Account 1 earns 0.25% interest compounded monthly, and account 2

earns 0.25% simple interest monthly. Write two functions that model the balances B1 and B2 of both accounts, in dollars, after t months.

________________________________________

________________________________________

5. An initial population of 1000 bacteria

increases by 25% each day.

a. Is the population growth best

modeled by a linear function or an exponential function? Explain.

________________________________________

________________________________________

b. Write a function that models the

population P after t days.

________________________________________

6. The value of a stock over time is shown

in the table. Write an exponential function

that models the value V, in dollars, after t years. Show your work.

________________________________________

________________________________________

________________________________________

Weeks Amount 1 $30 2 $45 3 $60 4 $75 5 $90 6 $105

x f(x) 2 1 4 5 6 9

Time, in years

Value, in dollars

0 18.00 1 16.20 2 14.58 3 13.12 4 11.81 5 10.63

Name ________________________________________ Date ___________________ Class __________________



7. The number of seats in each row of an

auditorium can be modeled by an arithmetic sequence. The 5th row in this auditorium has 36 seats. The 12th row in this auditorium has 64 seats. Write an

explicit rule for an arithmetic sequence that models the number of seats s in the nth row of the auditorium. Show your work.

________________________________________

________________________________________

8. The art club is creating and selling a

comic book as part of a fundraiser. The graph shows the profit P earned from selling c comic books.

a. Use the graph to write a linear

function P(c) that models the profit P from selling c comic books.

________________________________________

b. What is the real-world meaning

of the slope and P-intercept of

your function?

________________________________________

c. How many comic books does the

club have to sell in order to make $375? Show your work.

________________________________________

________________________________________

9. The neck of a guitar is divided by frets in such a way that pressing down on each

fret changes the note produced when the guitar is played. The first fret of a guitar is placed 36.35 mm from the end of the guitar’s neck. The second fret is placed

34.31 mm from the first fret. The distances, d, in millimeters, of the first four frets relative to the previous fret are shown in the graph below.

a. Consider the sequence of distances

between the frets. Is the sequence

arithmetic or geometric? Find a common difference or ratio to justify your answer.

________________________________________

________________________________________

b. Write an explicit rule for d(n), the

distance between fret n and the fret below it. Show your work.

________________________________________

c. Use your rule from part b to

determine the distance between the 19th and 20th frets.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



F.LE.3*

SELECTED RESPONSE Select all correct answers.

1. The value VA of stock A t months after it

is purchased is modeled by the function

VA(t) = t2 + 1.50. The value VB of stock B t months after it is purchased is modeled by the function VB(t) = 10(1.25)t. Based on the model, for which t-values is the

value of stock B greater than the value of stock A?

t = 5

t = 6

t = 7

t = 11

t = 12

Select the correct answer.

2. f(x) = 2x2 + 2 and g(x) = 2x + 1 + 2 are

graphed on the grid below. For what x-values is g(x) > f(x)?

x > 4

x > 2

0 < x < 2 and x > 4

2 < x < 4

3. As x increases without bound, which of

the following eventually has greater

function values than all the others for the same values of x?

f(x) = 3x2

f(x) = 2x3

f(x) = 3(2x)

f(x) = 3x + 2


4. Two websites launched at the beginning

of the year. The number of visits A(t) to website A is given by some exponential

function, where t is the time in months after the website is launched. The number of visits B(t) to website B is given by some quadratic function. The graph of

each function is shown below. For each of the given t-values, compare A(t) and B(t).

a. t = 2 A(t) < B(t) A(t) > B(t) b. t = 3 A(t) < B(t) A(t) > B(t) c. t = 4 A(t) < B(t) A(t) > B(t) d. t = 5 A(t) < B(t) A(t) > B(t) e. t > 12 A(t) < B(t) A(t) > B(t)

Name ________________________________________ Date ___________________ Class __________________




5. The population A of town A and the

population B of town B t years after 2000 is described in the table.

a. Write functions for A(t) and B(t).

________________________________________

________________________________________

b. Use your functions from part a to

complete the table, rounding to the nearest person.

c. If the populations continue to

increase in the same way, how do the populations compare for every

year after 2008? Explain how you can tell without calculating the populations for every year.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

6. Let f(x) = x + 4, g(x) = x4, and h(x) = 4x for

x ≥ 0.

a. Graph f(x) and h(x).

b. Graph g(x) and h(x).

c. How do the values of h(x) compare to the values of f(x) and g(x) as x increases without bound?

________________________________________

________________________________________

d. Use the graphs and your answer

from part c to make a conjecture about how the values of exponential functions compare to the values of

linear and polynomial functions as x increases without bound.

________________________________________

________________________________________

Time, t (years)

Town A population,

A(t)

Town B population,

B(t) 0 1500 1500 1 1800 1725 2 2100 1984 3 2400 2281 4 2700 2624 5 3000 3017 6 3300 3470 7 8

Name ________________________________________ Date ___________________ Class __________________



F.LE.5*


1. The function A(d) = 0.45d + 180 models

the amount A, in dollars, that Terry’s

company pays him based on the round-trip distance d, in miles, that Terry travels to a job site. How much does Terry’s pay increase for every mile of travel?

$0.45

$180.00

$180.45

$180.90

2. Drake is considering buying one of the

four popular e-readers where the e-reader’s premium services is a monthly

charge. The functions A1(t) = 5t + 350, A2(t) = 10t + 250, A3(t) = 499, and A4(t) = 15t + 179 model the total amount of money A, in dollars, that Drake spends

after buying the e-reader and subscribing to t months of the e-reader’s premium services. Which e-reader has the greatest monthly subscription cost?

E-reader 1 with cost A1(t)




3. Each bacterium in a petri dish splits into

2 bacteria after one day. The function

b(d) = 600 i 2d models the number of

bacteria b in the petri dish after d days. What is the initial number of bacteria in

the petri dish?

2

300

600

1200


4. The function a(t) = 44,000(1.045)t models

Johanna’s annual earnings a, in dollars, t years after she starts her job. Which of the following statements are true about Johanna’s salary?

Johanna initially earns

$44,000 per year.

Johanna initially earns

$45,980 per year.

Johanna’s salary increases by

1.045% per year.


4.5% per year.


104.5% per year.


5. The function h(t) = −1200t + 15,000

models the height h, in feet, of an

airplane t minutes after it starts descending in order for it to land. What is the height of the airplane when it begins to descend? Explain.

________________________________________

________________________________________

6. The function

P(r ) = 256 1

2⎛⎝⎜

⎞⎠⎟

r

represents

the number of players P remaining after r single-elimination rounds of a tennis tournament.

a. What is the initial number of players

in the tournament? Explain.

________________________________________

b. What fraction of players remaining

after r − 1 rounds are eliminated in

the rth round? Explain.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7. The function P(r) = 1250(0.98)t models

the premium P, in dollars, that Steven pays for automotive insurance each year

after having the insurance for t years.

a. What is the amount that Steven

pays for the first year of his insurance coverage?

________________________________________

________________________________________

b. What is the percentage decrease

of Steven’s premium every year? Explain.

________________________________________

________________________________________

________________________________________

8. A family is traveling in a car at a constant

average speed during a road trip. The function d(t) = 65t + 715 models the distance d, in miles, the family is from their house t hours after starting to drive

on the second day of the road trip.

a. At what average speed is the family’s

car traveling? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

b. What is the distance between the

family’s house and the point where they started driving on the second day? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

9. A census from the government

determines the official population of jurisdictions. The census is taken once

every decade. The function A(c) = 50,600(1.08)c models the official value for the population of city A, where c is the number of censuses taken since

the first census. Similarly, B(c) = 75,850(1.069)c models the official value for the population of city B.

a. Which city had a larger population in

the first census? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

b. Which city’s official value for its population is growing at a faster rate

between the censuses? Explain.

________________________________________

________________________________________

________________________________________

________________________________________


Algebra 1 Teacher Guide 39 Common Core Assessment Readiness

F.IF.1 Answers 1. B

2. A

3. B, D, F, G

4. A function assigns each value from the domain to exactly one value in the range. The relation is not a function because February has 28 days in a common year and 29 days in a leap year.

Rubric 1 point for stating its not a function;

2 points for explanation

5. The table represents a function.

The domain is {−2, −1, 0, 1, 2}.

The range is {2, 6, 10, 14, 18}.

Rubric 1 point for answer; 1 point for domain;

1 point for range

6. The y-value associated with x = −2 is 4.

The y-value associated with x = 0 is 3.

The y-value associated with x = 2 is 2.

If y = f(x), then the x-values are in the domain of f(x), and the y-values are in the range of f(x). Rubric 1 points for each y-value;

1 point for stating the x-values are in the domain of f(x); 1 point for stating the y-values are in the range of f(x)

7. The domain of the function is the set of all real numbers.

The range is the set of real numbers

greater than −3.

Rubric 1 point for the domain; 2 points for the range

8. a. This is a function because no coin has

more than one monetary value. The

domain is the set of coins {penny, nickel, dime, quarter, half dollar}. The range is the set of monetary values assigned to each coin,

{$0.01, $0.05, $0.10, $0.25, $0.50}. (Students may or may not include half dollar and dollar coins in their example. Assign full credit as long as

penny, nickel, dime, and quarter are included.)

b. This is not a function because each bill

is equivalent to many different combinations of coins. For example, a 1 dollar bill is equivalent to 100 pennies, but it is also equivalent to

10 dimes.

Rubric a. 1 point for answer;

1 point for explanation;

1 point for the domain; 1 point for the range

b. 1 point for answer;

1 point for explanation

Name ________________________________________ Date ___________________ Class __________________



F.IF.2 Answers 1. A

2. C

3. C

4. B, D, F, H

5. C(15) = 25(15) = 375

This value represents the production cost of 15 graphing calculators. So, it costs $375 to produce 15 graphing calculators.

Rubric 1 point for value; 1 point for interpretation

6. f(−2) = 13(−2) − (−2)2 = −26 − 4 = −30

f(−1) = 13(−1) − (−1)2 = −13 − 1 = −14

f(0) = 13(0) − 02 = 0 − 0 = 0

f(1) = 13(1) − 12 = 13 − 1 = 12

f(2) = 13(2) − 22 = 26 − 4 = 22

The range of the function is

{−30, −14, 0, 12, 22}.

Rubric 0.5 point for each value in the range; 0.5 point for work

7. a. The domain of the function is

{2, 3, 4, 5, 6, 7}.

b. V(2) = 23 = 8 cubic feet

V(3) = 33 = 27 cubic feet

V(4) = 43 = 64 cubic feet

V(5) = 53 = 125 cubic feet

V(6) = 63 = 216 cubic feet

V(7) = 73 = 343 cubic feet

Rubric a. 1 point

b. 0.5 point for each value

8. a. The profit function is:

P(n) = 149.99n − 25(99.50)

= 149.99n − 2487.50

b. The domain of the function is all whole

numbers between 0 and 25, inclusive. The store cannot sell a negative

number of televisions and they can only sell up to the number in stock, which is 25.

c. The store will make a profit of

$1,262.25.

Rubric a. 1 point

b. 1 point for domain; 1 point for explanation

c. 1 point

9. a. Set p(t) equal to zero and solve for t.

0 = −8t +100−100 = −8t

t = 12.5

It would take 12.5 minutes for the printer to use all 100 sheets.

b. The domain of the function is all

values of t, where 0 ≤ t ≤ 12.5. The printer takes 12.5 minutes to print all 100 pages, so the upper bound on t is

12.5. The printer starts printing at 0 minutes, so the lower bound is 0.

c. The range of the function is all values

of p(t), where 0 ≤ p(t) ≤ 100. There are 100 sheets of paper in the printer at the start, so the upper bound on p(t) is

100. There cannot be a negative number of sheets, so the lower bound on p(t) is 0.

d. The printer will have

p(7) = −8(7) + 100 = −56 + 100 = 44 sheets of paper left. So, Tanya’s report is 100 − 44 = 56 pages long.

Rubric a. 1 point for answer; 1 point for

explanation

b. 1 point for domain; 1 point for

explanation

c. 1 point for range; 1 point for

explanation

d. 1 point for answer; 1 point for work



F.IF.3 Answers 1. B

2. D

3. A, C

4. B

5. D

6. F

7. A

8. E

9. a. f(n) = n2 + 1

b. f(14) = 142 + 1 = 197

Rubric a. 1 point

b. 1 point

10. a Since the domain starts with 1, f(3) is

the third term of the sequence, which

is 45

.

b. When the domain starts with 0, f(3) is

the fourth term of the sequence, 56

.

Rubric a. 1 point for answer; 1 point

for explanation

b. 1 point

11. a. Each term in the Fibonacci sequence

is the sum of the previous two terms,

and the first two terms are 1. A recursive function that describes this is f(0) = f(1) = 1, f(n) = f(n − 1) + f(n − 2), n ≥ 2.

b. 2, 2, 4, 6, 10

c. Each term in the new sequence is still

the sum of the previous two terms (4 = 2 + 2, 6 = 4 + 2, 10 = 6 + 4, and so on), so the function from part b can be described as f(0) = f(1) = 2,

f(n) = f(n − 1) + f(n − 2), n ≥ 2.

Rubric a. 1 point

b. 1 point

c. 2 points for explanation

12. a. f(n) = 2n − 1

b. f(1) = 1, f(n) = f(n − 1) + 2 for n ≥ 2 and n is an integer.

Rubric a. 2 points

b. 2 points



F.IF.4* Answers 1. C

2. A, C, G

3.

The C(t)-intercept is $15, which is the cost for sending up to 1000 texts.

Rubric 2 points for graph; 1 point for intercept;

1 point for interpretation

4. The profit increases as the orchard goes from 0 to 40 trees. Then, the profit decreases from 40 to 80 trees. The owner of the orchard earned the least profit when there were no trees planted and when there were 80 trees planted. The most profit was earned when there were 40 trees planted.

Rubric 2 points for description of relationship; 2 points for stating where the orchard owner earned the least profit;

1 point for stating where the orchard owner earned the most profit

5. a.

b. The function is decreasing for x < 0 and increasing for 0 < x.

c. f(x) is positive for all values of x except 0.

d. f(x) will never be negative because

absolute value can never be negative.

Rubric a. 1 point

b. 1 point for stating where f(x) decreases;

1 point for stating where f(x) increases

c. 1 point

d. 2 points



F.IF.5* Answers 1. C

2. D

3. C

4. a. The domain is t such that 0 ≤ t ≤ 7.

b. The domain represents the time that the object is in the air.

Rubric 1 point for each part

5. The domain is the real numbers.

The range is the real numbers greater than −2.

Rubric 1 point for the domain; 1 point for the range

6. a. P(c) = 350c − 1800

b. The domain of P(c) is the whole

numbers. The company cannot sell a negative number of the tablet computers and they cannot sell a fractional number of tablet computers.

c. −1800, −1450, −1100, −750, −400, −50, 300, 650

Rubric a. 2 points for the function

b. 1 point for the domain; 1 point for the explanation;

c. 2 points for range values

7. Brand A

A(h) = 4.19h

The domain of A(h) is the nonnegative real numbers since brand A can be purchased in any nonnegative amount from the deli counter.

Brand B

B(h) = 4.79h

The domain of B(h) is {0, 0.5, 1, 1.5, …} since brand B can only be purchased in increments of either 0.5 pound or 1 pound.

Rubric 1 point for each function rule;

1 point for each domain; 1 point for each explanation



F.IF.6* Answers 1. B

2. A

3. C

4. C, D, E

5. a. No

b. Yes

c. No

d. Yes

e. No

6. a. Anchorage: about −5.6 minutes of

daylight per day

Los Angeles: about −2.0 minutes of

daylight per day

b. On average, Anchorage loses about

5.6 minutes of daylight each day during the month of October, while Los Angeles loses about 2 minutes of daylight each day.

c. Since October 17 is 16 days after October 1, evaluate the expression 711 + (−2.0)(16) to get 679 minutes, or

11 hours 19 minutes, of daylight on October 17. If the sun rises at 7:00 A.M. that day, then it sets about 11 hours and 19 minutes later, or at

6:19 P.M.

Rubric a. 0.5 point for each average rate of

change;

b. 1 point

c. 1 point for finding the minutes of

daylight; 1 point for the description of how to find the minutes of daylight;

1 point for the time of sunset

7. a. The average growth rate between

weeks 2 and 3 is about

4000 − 2000

3 − 2= 2000

1=

2000 bacteria per week.

b. The average growth rate between weeks 3 and 4 is about

8000 − 4000

4 − 3= 4000

1=


c. The average growth rate between weeks 4 and 5 is about

16000 − 8000

5 − 4= 8000

1=


d. The average growth rate is doubling

as each week passes.

2(2000) = 4000 bacteria per week,

2(4000) = 8000 bacteria per week

e. The average growth rate between

weeks 5 and 6 will probably be 16,000 bacteria per week if the pattern continues.

Rubric a. 0.5 point

b. 0.5 point

c. 0.5 point

d. 1 point for answer;

2 points for justification

e. 0.5 point



F.IF.7a* Answers 1. B

2. A

3. a. R(n) = 5.25n

b. Since Sally is selling 1 necklace at a time and cannot sell negative necklaces, a reasonable domain for this function is the whole numbers.

c.

5–5 n

25

–25

R(n)

d. The n- and R-intercepts are both 0.

The intercept indicates that Sally

will earn no revenue if she sells no necklaces.

Rubric a. 1 point

b. 1 point

c. 1 point

d. 1 point for the intercept; 1 point for the explanation

4. a. The t-intercepts are 0 and 5. These intercepts indicate that the object has

a height of 0 meters when the object is thrown (t = 0) and again at 5 seconds after it is thrown.

The h-intercept is the same as the first

t-intercept.

b. The vertex is (2.5, 30.625).

c. The vertex is a maximum. This means that the maximum height of the object

is 30.625 feet.

d.

Rubric a. 1 point for each t-intercept;

0.5 point for each interpretation

b. 1 point for the vertex

c. 0.5 point for the answer;

0.5 point for the interpretation

d. 2 points for correct graph

5. One side of the rectangular enclosure is s. Let the other side of the enclosure be x. The perimeter of the combined

enclosures is 1200 = 5s + 2x. Solve for x:

1200 = 5s + 2x1200 − 5s = 2x

0.5(1200 − 5s) = x600 − 2.5s = x

The width of the rectangular enclosure is

s + x = s + 600 − 2.5s = 600 − 1.5s. The combined area of the enclosures is

A(s) = s(600 −1.5s)= 600s −1.5s2

= −1.5s2 + 600s



The square enclosure will be 200 feet by

200 feet. The rectangular enclosure will be 100 feet by 200 feet. The vertex of the function, (200, 60000), is a maximum.

This means that the combined area of the enclosures is maximized when s = 200. Since s is the side length of the square, the square is 200 feet by 200 feet. Since

the rectangle shares a side with the square, one of its dimensions is 200 feet. The other is given by the expression 600 − 2.5s.

600 − 2.5(200) = 600 − 500

= 100

Thus, the rectangle is 100 feet by

200 feet.

Rubric 2 points for the function; 1 point for the graph; 1 point for each set of dimensions;

2 points for explanation involving the vertex



F.IF.7b* Answers 1. B

2. D

3. B

4.

The domain is the real numbers and the

range is {−2, 1, 4}.

Rubric 1 point for graph;

1 point each for the domain and range

5.

The reaction time increases as the distance increases. The graph of t(d) is increasing for d > 0.

Rubric 1 point for graph;

1 point for answer; 1 point for explanation involving graph

6. Possible answer:

f (x) =

−1 x < 00 0 ≤ x <11 1≤ x < 22 x ≥ 2

⎧

⎨⎪⎪

⎩⎪⎪

Rubric 3 points for the function;

1 point for the graph

7.

The function is increasing on its entire domain. Thus, the function is never decreasing.

Rubric 1 point for the graph;

2 points for recognizing the graph is always increasing



F.IF.7e* Answers 1. C

2. B

3. A, C, E

4. Possible answer: An exponential function has either one x-intercept or no x-intercepts. The functions f(x) = 2x + 2 and g(x) = 2x − 2 illustrate this in the following graph. f(x) = 2x + 2 has no x-intercepts, while g(x) = 2x − 2 has one x-intercept.

Rubric 1 point for stating such a function can

have no x-intercepts; 1 point for stating such a function can have 1 x-intercept; 1 point each for example graphs

illustrating both possibilities (no symbolic definition of example functions necessary)

5. a.

b. The V(t)-intercept is 1200. This is the value of the copier at the time of

purchase, $1200.

Rubric a. 2 points for the graph

b. 1 point for the V(t)-intercept;

1 point for the interpretation



F.IF.8a Answers 1. B

2. B

3. B, C, E

4. a. False

b. True

c. False

d. True

e. True

5. a.

f (x) = 4x2 + 4x −15= 4x2 +10x − 6x −15= 2x(2x + 5)− 3(2x + 5)= (2x − 3)(2x + 5)

The zeros of the function are x = 3

2

and x = − 5

2.

b. The vertex is halfway between the

zeros of the function, so the

x-coordinate is − 1

2. The value of the

function at x = − 1

2 is

4 − 1

2⎛⎝⎜

⎞⎠⎟

2

+ 4 − 12

⎛⎝⎜

⎞⎠⎟−15 = −16.

The vertex of f(x) is

− 1

2, −16

⎛⎝⎜

⎞⎠⎟. The

coefficient of x2 is positive, so the

parabola opens up, and the vertex is the minimum value.

Rubric a. 1 point for factoring; 0.5 point for

each zero

b. 1 point for coordinates of the vertex;

1 point for stating that the vertex is a minimum; 1 point for explanation

6. a. Miguel is correct in saying that the

function has no x-intercepts. However, the axis of symmetry can still be found by completing the square and finding

the vertex. The axis of symmetry passes through the vertex.

b. Complete the square:

f (x) = −2x2 −16x − 34= −2 x2 + 8x( )− 34

= −2 x2 + 8x +16 −16( )− 34

= −2 x2 + 8x +16( ) + 32− 34

= −2 x + 4( )2 − 2

The vertex of the function is (−4, −2),

so the axis of symmetry is x = −4.

Rubric a. 1 point

b. 1 point for work; 1 point for answer

7. a.

h(x) = − 9125

x2 + 45

= − 9125

x2 − 625( )= − 9

125(x − 25)(x + 25)

The zeros of the function occur where

the sides of the arch are at the water level. They are 25 feet to the left and

right of the center of the bridge, so the bridge is 50 feet long.

b. The coefficient of x2 is negative, so the

vertex is a maximum value of the function. The vertex is halfway between the zeros of the function, at

x = 0. h(0) = − 9

125(0)2 + 45 = 45

feet,

so the sailboat will not be able to pass

under the bridge.


explanation involving the zeros

b. 1 point for answer; 1 point for explanation involving the vertex as a maximum



F.IF.8b Answers 1. A

2. B

3. A, C, E, F, H

4. a. Not equivalent

b. Equivalent

c. Equivalent

d. Not equivalent

e. Equivalent

f. Not equivalent

5. a.

P(t) = 3.98(1.02)t

= 3.98(1+ 0.02)t

b. The value of r is 0.02. This means

that the population increases by 2% annually.

Rubric a. 1 point

b. 1 point for answer; 1 point for interpretation

6.

g(x) = 200 4x−1( )= 200 4x • 4−1( )= 200 4x

4⎛

⎝⎜⎞

⎠⎟

= 14

200 4x( )( )= 1

4f (x)( )

The function values of g(x) are 14

of the

corresponding values of f(x). Rubric 2 points for work transforming g(x); 1 point for answer

7. a.

V (t) = 1500(1.035)t

= 1500(1+ 0.035)t

The annual interest rate is 3.5%.

b.

V (t) = 1500(1.035)t

= 1500 1.0355( )t5

≈1500(1.19)t5

The interest rate over 5 years is

about 19%.

Rubric a. 1 point

b. 1 point for answer; 1 point for

appropriate work

8. a.

B(t) = 850 1.04( )t= 850(1+ 0.04)t

The annual interest rate is 4%.

b.

B(t) = 850 1.04( )t

= 850 1.041

12⎛⎝⎜

⎞⎠⎟

12t

≈ 850(1.0033)12t

The monthly interest rate is

approximately 0.33%.

c. Rebecca’s account will have a larger balance after 6 months. Since

0.35 > 0.33, Rebecca’s account earns a greater amount of interest each month.

Rubric a. 1 point for rewriting the function;

1 point for answer

b. 1 point for rewriting the function;

1 point for answer

c. 1 point for answer;




F.IF.9 Answers 1. C

2. D

3. B, E

4. Both f(x) and g(x) are defined on the domain from 1 to 4. However, f(x) is only defined for the whole numbers 1, 2, 3, and 4, while g(x) is defined for all real numbers between 1 and 4, inclusive. The range of f(x) is the set {4, 6, 10, 18}. The

range of g(x) is g(1) ≤ g(x) ≤ g(4), or 4 ≤ g(x) ≤ 19. The initial value for both functions is f(1) = 4 = 12 + 3 = g(1).

Rubric 1 point for comparing domains; 1 point for comparing ranges; 1 point for comparing initial values

5. The maximum value of the function

shown in the graph is f(6) = 4. The maximum value of the function in the table is g(0) = 5. Since the maximum known value for g(x) is greater than the maximum value of f(x), g(x) has a greater maximum value on the domain −6 ≤ x ≤ 6.

Rubric 1 point for answer; 1 point for explanation

6. a. Plan A costs more for 3 months. The

cost of plan A for 3 months is 70(3) = $210, and the cost of plan B for 3 months is $200.

b. 5 months. The cost of plan A for

1 through 6 months is A(1) = $70, A(2) = $140, A(3) = $210, A(4) = $280,

A(5) = $350, and A(6) = $420. Comparing these values to the corresponding values of B(t), the first time the difference is greater than

50 is when t = 5.

Rubric a. 1 point for answer; 1 point

for explanation

b. 1 point for answer; 2 points for

explanation comparing function values



F.BF.1a* Answers 1. B

2. C

3. C

4. A, D, E

5. a. T(n) = 0.1(2)n

b.

A(n) = 10,000 1

2⎛⎝⎜

⎞⎠⎟

n

Rubric a. 1 point

b. 1 point

6. H(n) = 4n

Rubric 2 points

7. a. Possible answer:

1. Multiply the population from the

previous year by 0.05 to find the amount the population increases.

2. Add this amount to the population

from the previous year.

b. P(0) = 300 and P(t + 1) = 1.05P(t)

for t ≥ 0

Rubric a. 2 points

b. 1 point

8. a. The perimeter of the enclosed area is

500 = 2w + 2 , where is the length of

the enclosed area. Solve for :

2 = 500 − 2w

= 250 −w

The area in terms of w is as follows:

A(w) = w= (250 −w)w= 250w −w2

= −w2 + 250w

b. The graph of the function

A(w) = −w2 + 250w is a parabola that opens down. The maximum is the function value at the vertex.

Complete the square to find the vertex:

A(w) = −w2 + 250wA(w) = −(w2 − 250w)

A(w)−1252 = −(w2 − 2(125)w +1252)A(w) = −(w −125)2 +1252

A(w) = −(w −125)2 +15,625

The vertex occurs at (125, 15,625). When the width is 125 feet, the area Simon can enclose is 15,625 square

feet. The length of the rectangle is 250 − w = 250 − 125 = 125 feet.

Rubric a. 1 point for function;

2 points for appropriate work





F.BF.1b* Answers 1. C

2. B

3. A, E

4. a. Quadratic

b. Linear

c. Neither

d. Neither

5.

f (x)+ g(x) = (x2 + x − 6)+ (x2 − 4)= 2x2 + x −10

f (x)− g(x) = (x2 + x − 6)− (x2 − 4)= x2 + x − 6 − x2 + 4= x − 2

Rubric 1 point for each answer

6. a. d1(t) = 880t b.

d2(t) = 400(45 − t)= 18,000 − 400t

c.

d(t) = d1(t)+ d2(t)= 880t +18,000 − 400t= 480t +18,000

Rubric a. 1 point

b. 1 point

c. 1 point

7. Trina’s account: 1500(1.05)t

Pablo’s account: 1800(1.025)t

D(t) = 1500(1.05)t −1800(1.025)t

( D(t) = 1800(1.025)t −1500(1.05)t is

also correct.)

Rubric 3 points for writing a correct difference function

8. a. A(t) = 15,000(1.025)t

b. B(t) = 15,000(0.965)t

c.

A(t)+B(t) = 15,000(1.025)t +15,000(0.965)t

= 15,000(1.025t + 0.965t )

This function describes the combined

populations of towns A and B t years after 2000.

A(t)B(t)

= 15,000(1.025)t

15,000(0.965)t

= (1.025)t

(0.965)t

= 1.0250.965

⎛⎝⎜

⎞⎠⎟

t

≈1.062t

This function describes the ratio of the

population of town A to the population of town B t years after 2000.

Rubric a. 1 point

b. 1 point

c. 1 point for each function; 1 point for

each interpretation



F.BF.2* Answers 1. B

2. D

3. B, C, F

4. a. t(1) = 40, t(d) = t(d − 1) + 5, for

2 ≤ d ≤ 10

b. t(d) = 5(d − 1) + 40

c.

t(8) = 5(8 −1)+ 40= 5(7)+ 40= 35 + 40= 75

Calvin practices for 75 minutes on the

8th day.

Rubric a. 1 point

b. 1 point

c. 0.5 point for answer; 0.5 point for

showing work

5. a. This sequence is geometric because

the ratios of consecutive terms are approximately equal.

54.15

57= 0.95,

51.4454.15

≈ 0.95,

48.8751.44

≈ 0.95

The common ratio is

approximately 0.95.

b. s(t) = 57(0.95)t − 1

c. s(1) = 57, s(t) = s(t − 1) i 0.95, for t ≥ 2

d. The speed of the car is 60 feet per second when it begins to coast.

Substitute 0 for t in the explicit formula,

s(t) = 57(0.9)t − 1.

s(0) = 57(0.95)0 − 1

= 57(0.95)−1

= 60

Rubric 1 point for each part

6. a. An arithmetic sequence models this

situation because there is a common

difference between every term.

334 − 306 = 28 362 − 334 = 28

390 − 362 = 28

b. Since the common difference is 28, the first term of the sequence is p = 2,

and c(2) = 306, an explicit formula that models this situation is c(p) = 306 + 28(p − 2) for p ≥ 2.

A recursive formula that models this

situation is c(2) = 306, c(p) = c(p − 1) + 28, for p ≥ 3.

c. Substitute 44 for p in the explicit formula, c(p) = 306 + 28(p − 2).

c(p) = 306 + 28(44 − 2)= 306 + 28(42)= 306 +1176= 1482

It would cost $1,482 for 44 people to

attend the party.


justification

b. 1 point for explicit formula;

1 point for recursive formula; 1 point for showing work

c. 0.5 point for answer; 0.5 point for

showing work



F.BF.3 Answers 1. B

2. C

3. Possible answer: The graph of f(x) is reflected about the y-axis, shifted left 1 unit, vertically stretched by a factor of 2, reflected about the x-axis, and shifted up 3 units to obtain g(x).

Rubric 5 points for transformations; 1 point for graph

4. The slope m acts as a vertical stretch or shrink factor. If 0 < |m| < 1, then the graph of g(x) is a vertical shrink of the graph of f(x) by a factor of m. If |m| > 1, then the graph of g(x) is a vertical stretch of the graph of f(x) by a factor of m. The sign of the slope can also transform the graph of g(x). If m < 0, then the graph of g(x) is a reflection about the x-axis of the graph of f(x). If m > 0, no reflection occurs.

Rubric 2 points for description of how m can be a shrink or a stretch (either vertical or horizontal);

1 point for description of how m can be a reflection

5. a. f(x) = x; vertical shift up; g(x) = x + 3

Alternate answer: f(x) = x; horizontal

shift left; g(x) = x + 3

b. f(x) = 2x; vertical shift down;

h(x) = 2x − 2

Rubric a. 0.5 point for parent function; 1 point for

transformation; 1 point for rule

b. 0.5 point for parent function; 1 point for

transformation; 1 point for rule

6. a.

g(x) = − 12

x2 − 2x + 2

= − 12

(x2 + 4x)+ 2

= − 12

(x2 + 4x + 4 − 4)+ 2

= − 12

(x + 2)2 − 4⎡⎣ ⎤⎦ + 2

= − 12

(x + 2)2 + 2+ 2

= − 12

(x + 2)2 + 4

b. Possible answer: The graph of f(x) is shifted left 2 units, vertically shrunk by

a factor of 12

, reflected across the

x-axis, and shifted up 4 units.

c.


1 point for reasonable work

b. 2 points for transformations

c. 1 point



F.BF.4a Answers 1. B

2. D

3. A, B, D

4.

f (x) = −13x + 52y = −13x + 52

y − 52 = −13xy − 52−13

= x

− 113

y + 4 = x

− 113

x + 4 = y

g(x) = − 113

x + 4

The inverse of f(x) is g(x) = − 1

13x + 4. To

find a value of x such that f(x) = 182, find g(182).

g(182) = − 113

(182)+ 4

= −14 + 4= −10

When x = −10, f(x) = 182.

Rubric 1 point for finding the inverse of f(x); 1 point for work; 1 point for using it to find x; 1 point for work

5. a. A(r) = 3r + 15

b. r(A) = 1

3A− 5

A = 3r +15A−15 = 3rA−15

3= r

r = 13

A− 5

c. This function represents the number of

rides r you could go on if you plan to spend A dollars at the carnival.

Rubric a. 1 point

b. 1 point for answer; 1 point for work

c. 2 points

6. a.

f (x) = 3x − 6y = 3x − 6

y + 6 = 3xy + 6

3= x

13

y + 2 = x

13

x + 2 = y

g(x) = 13

x + 2

b.

c. The graphs of f(x) and g(x) are

reflections across the line y = x. Rubric

a. 1 point for answer; 1 point for work

b. 1 point

c. 1 point



7. a.

f (x) = mx + by = mx + b

y − b = mxy − b

m= x

1m

y − bm

= x

1m

x − bm

= y

g(x) = 1m

x − bm

b. g(x) = 1

4x − 11

4

c. No; the function g(x) = 1

mx − b

m is not

defined for linear functions with a

slope of 0 because the fractions with m in the denominator are not defined for m = 0. Functions of the form f(x) = c do not have inverses.

Rubric a. 1 point for answer; 1 point for work

b. 1 point

c. 1 point for answer; 1 point for explanation; 1 point for general form



F.LE.1a* Answers

1. B

2. C

3. A, D, E

4. A

5. G

6. F

7. H

8. E

9.

x2 − x1 = x4 − x3 Givenm(x2 − x1) = m(x4 − x3 ) Multiplication property of equalitymx2 − mx1 = mx4 − mx3 Distributive property

mx2 + b − mx1 − b = mx4 + b − mx3 − b Addition and subtraction properties(mx2 + b) − (mx1 + b) = (mx4 + b) − (mx3 + b) Distributive property

f (x2) − f (x1) = f (x4 ) − f (x3 ) Definition of f (x)

Rubric

1 point for each correctly completed part

10. a. Time, t (years)

Salary, S (dollars)

1 39,500 2 41,000 3 42,500 4 44,000 5 45,500

b. Sandra’s salary increases by $1500 each year.

S(2) − S(1) = 41,000 − 39,500 = 1500

S(3) − S(2) = 42,500 − 41,000 = 1500

S(4) − S(3) = 44,000 − 42,500 = 1500

S(5) − S(4) = 45,500 − 44,000 = 1500

Rubric

a. 2 points

b. 1 point for answer; 1 point for appropriate work



11. a. P(0) = 3500(0.97)0 = 3500 people

P(1) = 3500(0.97)1 = 3395 people

P(1)P(0)

=33953500

= 0.97

P(2) = 3500(0.97)2 ≈ 3293 people

P(2)P(1)

≈32933395

≈ 0.97

The population changes by the same factor over each 1 year interval.

b.

P(2)P(0)

=32933500

≈ 0.94

P(3) = 3500(0.97)3 ≈ 3194 people

P(3)P(1)

≈31943395

≈ 0.94

The population changes by the same factor over each 2 year interval.

Rubric a. 1 point for the factor between 2000 and 2001; 1 point for the factor between 2001 and

2002; 1 point for work

b. 1 point for the factor between 2000 and 2002; 1 point for the factor between 2001 and

2003; 1 point for work



F.LE.1b* Answers 1. B

2. B

3. B, D, E

4. h(x) changes at a constant rate per unit change in x.

25 − 31= −619 − 25 = −613 −19 = −67 −13 = −6

The function values decrease by 6 per unit change in x. Rubric 1 point for answer; 2 points for

explanation using function values

5. Yes, Samantha’s hourly pay grows at a rate of $0.25 per hour each month. The increase is always the same, so her pay increases at a constant rate per unit change in month.

Rubric

1 point for answer; 1 point for explanation

6.

4 miles2 hours

= 2 miles per hour;

1.5 miles45 minutes

= 1.5 miles34

hour= 2 miles per hour

They hike at the same rate over both intervals, so they hike at a constant rate of 2 miles per hour.

Rubric 1 point for answer; 1 point for unit rate

7. a. Tim’s base pay increases by $1000

after the first year and by $1040 after

the second year, so it does not change at a constant rate.

b. Tim’s commission rate increases by

1.5% after the first year and increases by 1.5% again after the second year, so it changes at a constant rate.

Rubric a. 1 point for answer; 0.5 point for

explanation

b. 1 point for answer; 0.5 point for

explanation

8. a. Year Company A Company B

0 500 500 1 550 550 2 605 600 3 665 650

b. Company B’s workforce has a

constant rate of growth per unit change in year.

Company A:

550 − 500 = 50605 − 550 = 55665 − 605 = 60

Company B:

550 − 500 = 50600 − 550 = 50650 − 600 = 50

c. 650 + 50 = 700 workers

Rubric a. 0.5 point for each value

b. 1 point for Company A’s workforce; 1 point for Company B’s workforce;

1 point for correct conclusion

c. 1 point



F.LE.1c* Answers 1. C

2. C

3. A, C

4. f(x) changes at a constant factor per unit change in x.

128512

= 14

, 32

128= 1

4,

832

= 14

, and 28= 1

4

The function values of f(x) change by a

factor of 14

per unit change in x.

Rubric 1 point for answer; 2 points for explanation

5. Yes; the decay factor for each year is 0.5,

which can be written as 1 − 0.5 in the form 1 − r, where r is the decay rate per year. So, the number of nests decreases by 50% each year.

Rubric 1 point for answer; 2 points for explanation

6. Yes; 483.24

500≈ 0.9665,

467.05483.24

≈ 0.9665,

and 451.40467.05

≈ 0.9665

The decay factor 0.9665 can be written

as 1 − 0.0335 in the form 1 − r, where r is the decay rate per minute. The decay rate as a percent is 3.35%.

Rubric 1 point for answer; 1 point for decay factor; 1 point for showing work

7. The antique toy and the antique chair have values that grow by a constant factor relative to time.

Antique toy:

77.0070.00

= 1.1, 84.7077.00

= 1.1, and 93.1784.70

= 1.1

Antique chair:

108.00100.00

= 1.08, 116.64108.00

= 1.08, and

125.97116.64

≈1.08

The value of the antique toy increases at a faster rate because the value of the antique toy grows by a factor of 1.1 per year and the value of the antique chair grows by a factor of 1.08 per year.

Rubric 1 point for identifying the antiques that show constant rates; 1 point for explanation with supporting work; 1 point

for stating that the value of the antique toy increases at a faster rate; 1 point for explanation

8. a. Yes;

Company A:

126,000120,000

= 1.05,

132,300126,000

= 1.05, and

138,915132,300

= 1.05

Since the growth factor is 1.05, the growth rate is 0.05, so the number of visits company A’s website receives

grows by 5% per month.

b. No;

Company B:

153,000150,000

= 1.02,

157,590153,000

= 1.03, and

159,166157,590

≈1.01

Since the growth factor is not the same between each month, the

number of visits for company B’s website does not grow by a constant percent per month.

Rubric a. 1 point for answer; 2 points for

explanation

b. 1 point for answer; 2 points for

explanation



F.LE.2* Answers 1. B, C

2. C

3. D

4. B1 = 100(1.0025)t

B2 = 100 + 0.25t Rubric 1 point for each function

5. a. Exponential. The population each day

is 25% greater than the population on the previous day.

b. P(t) = 1000(1.25)t



b. 1 point

6. r = 16.20

18= 0.9

V (t) = a(0.9)t

18 = a(0.9)0

18 = aV (t) = 18(0.9)t

Rubric 1 point for answer; 2 points for work

7. s5 = 36, s12 = 64

d = 64 − 36

12− 5= 28

7= 4

sn = s1 + d(n −1)64 = s1 + 4(12−1)64 = s1 + 4420 = s1

sn = 20 + 4(n −1)

Rubric 1 point for correct sequence; 2 points for work

8. a. m = 150 − 60

30 − 20= 90

10= 9

y = mx + b60 = 9(20)+ b60 = 180 + b

−120 = b

The art club’s profit is modeled by the

function P(c) = 9c − 120.

b. The slope is 9, which means that each

comic book costs $9.

The P-intercept is −120, which could mean that the art club spends $120 on

supplies to make the comic books.

c. The art club needs to sell 55 comic

books to make $375.

375 = 9c −120495 = 9c55 = c

Rubric a. 1 point

b. 1 point for interpretation of slope;

1 point for interpretation of intercept

c. 1 point for answer; 1 point for work

9. a. Geometric. The ratio of consecutive

distances is

34.3136.35

≈ 32.3934.31

≈ 30.5732.39

≈ 0.944.

b.

d(n) = d(1) i (0.944)n−1

= 36.35 i (0.944)n−1

c.

d(n) = 36.35 i(0.944)n−1

d(20) = 36.35 i(0.944)20−1

= 36.35 i(0.944)19

≈12.16

The 20th fret is about 12.16 mm from

the 19th fret.

Rubric a. 1 point for answer; 1 point for ratio

b. 1 point for answer; 1 point for work

c. 1 point for answer; 1 point for work



F.LE.3* Answers

1. A, B, E

2. C

3. C

4. a. A(t) < B(t) b. A(t) < B(t) c. A(t) > B(t) d. A(t) > B(t) e. A(t) > B(t) 5. a. A(t) = 300t + 1500

B(t) = 1500(1.15)t

b. Time, t (years)

Town A population,

A(t)

Town B population,

B(t) 0 1500 1500 1 1800 1725 2 2100 1984 3 2400 2281 4 2700 2624 5 3000 3017 6 3300 3470 7 3600 3990 8 3900 4589

c. Town B will have a larger population

than town A. A increases by the same amount (300) each year. B increases by the same percent (15%) each year. 15% of 4589 is

about 688, so B will continue to increase by a greater amount than A each year after 2008.

Rubric

a. 1 point for each function

b. 0.5 point for each value calculated

c. 1 point for answer;


6. a.

b.

c. Initially, the values of h(x) are less than the values of f(x), but greater than

the values of g(x). Eventually, the values of h(x) exceed the values of both f(x) and g(x).

d. The value of an exponential function

may start out less than the values of a linear function or a polynomial function for the same inputs. As x increases,

the value of the exponential function will eventually be greater than the values of the linear and polynomial functions for the same inputs.

Rubric

a. 0.5 point for graphing each function

b. 0.5 point for graphing each function

c. 2 points for accurate comparison

d. 2 points for accurate conjecture



F.LE.5* Answers 1. A

2. D

3. C

4. A, D

5. At t = 0, the plane begins to descend. So, the height of the airplane, in feet, when it begins to descend is h(0) = 15,000.

Rubric 1 point for correct height with correct units; 1 point for explanation

6. a. 256. The value of P(0) is 256.

b. 12

. Since the decay rate, 12

, is the

ratio of players remaining after

r rounds to the ratio of players remaining after r − 1 rounds, the fraction of players eliminated in

the rth round is 1− 1

2= 1

2.





7. a. $1250

b. 2%. Since 0.98 is the decay factor, it can be rewritten as 1 − 0.02, where

0.02 is the decay rate. Notice that 0.02 is equal to 2%.

Rubric a. 1 point

b. 1 point for answer; 1 point for explanation

8. a. 65 miles per hour. The coefficient of t is equal to the speed, in miles per

hour, that the family’s car is traveling. Notice that the coefficient of t is 65.

b. 715 miles. The distance between the

family’s house and the point where they started driving on the second day is equal to d(0). Notice that d(0) = 715.





9. a. City B. The official value of city A’s

population for the first census and the official value of city B’s population for the first census is when c = 0. Since

A(0) = 50,600, the value of city A’s population for the first census is 50,600. Since B(0) = 75,850, the value of city B’s population for the first

census is 75,850.

b. City A. The growth factor for city A is 1.08 and the growth factor for city B

is 1.069.



b. 1 point for answer; 1 point for explanation

Date post:	01-May-2018
Category:	Documents
Upload:	dinhdan
View:	216 times
Download:	2 times

A1 MNLEAN881263 FIF1 - Mr. Davenport's Math … greater than 1. The domain is the set of integers n...

Documents