Alg. 1 – Unit 3 Notes

Unit 3 – Day 1: Represent Relations and Functions (O.C. 1-5)

Objectives: SWBAT represent functions

A. Vocabulary –

Function –

Function Notation –

Coordinate –

Domain –

Range –

State the domain, the range and whether or not the following set of data is a function.

1) {(1, 3) (-4, -2) (3, 3) (2, 9)} 2) {(0, 2) (1, -5) (-3, 1) (1, 6)}

Domain: __________ Domain: __________

Range: __________ Range: __________

Is it a function? __________ Is it a function? __________

3) {(-2, 2) (-1, -3) (2, -4) (4, -4) (0,0)}

Domain: __________

Range: __________

Is it a function? __________

4) Given the following relationship, answer the following

a) Write the following information as points

b) Write the Domain and Range as sets

c) Write each pair of coordinates in function notation.

d) Explain what happens if 4 went to 9 instead of 16.

e) Explain what would happen if 2 was paired with 4 and 1.

5) Given the following relationship, answer the following

a) Write the following information as points

b) Write the Domain and Range as sets

c) Write each pair of coordinates in function notation.

d) Explain why or why not this is a function. If it is not a

function, explain what needs to change to make it a

function.

Look at the following sets of points; explain if they are functions. Say why or why not.

III.

6) Fill in the table, graph the function, label the axis, state the domain and range, and lastly if it is a

function or not.

The cost of sending a text message is $0.10 per message. This can described by the function: ( )

.

Independent

variable

Number of

Messages

Dependent

Variable

( ) Calculation

Function

Notation

Coordinate

Notation

1

2

3

4

5

Domain: __________ Range: ____________ Function?: _______________

a) Looking at the previous table and graph, how much would 15 texts cost? 29? Explain your answer

in function notation.

b) Is it possible to have a bill of $3.45. Explain why?

c) Is it possible to connect the dots on this graph? What would it mean if we connected the dots with a

line?

d) Explain using words what ( ) means.

HOMEWORK

Unit 3 Day 1: Represent Relations and Functions

1. Use the diagram to right to find the following

Domain: ______________

Range: ______________

Is it a function? Why or Why not: _________________________________________________

2. Use the diagrams below to fill in the desired information below.

Domain: ______________ Domain: ______________

Range: ______________ Range: ______________

Is it a function? ______________ Is it a function? ______________

3. Given the following sets, determine the following

{( )( )( )( )( )( )} {( )( )( )( )( )( )}

Domain: ______________ Domain: ______________

Range: ______________ Range: ______________

Is it a function? ______________ Is it a function? ______________

4. Take all the whole numbers from 1 – 9; if they were paired with their opposites’, explain if it would be a

function.

5. Take the function ( ) , using the domains 0,1,2,3,4,5, explain the domain and range in

function form.

6. In the function above on #5, what would f (10) = 31 mean?

c. What does M(4) = 1 mean? ___________________________________________

c. What does T (6) = 24 mean? ___________________________________________

NOTES

Unit 3 – Day 2: Modeling with Functions (O.C. 1-6)

Objectives: SWBAT represent functions

A. Vocabulary~

Independent Variable-

Dependent Variable-

Given the following functions, identify the dependent variable and independent variable.

1) ( ) 2) ( )

3) Mattick’s DJ Company is hired for a dance. He charges $125.00 per hour plus $55.00 flat fee for his

assistant.

4) You buy a printer for $139, and have to pay $15 for each ink cartridge.

5)

Use the following financial situation to answer the following questions 6 – 9 .

Jenna received an interest free loan of $270 to buy a new TV. She plans to make monthly loan payments of

$30 per month until the loan is paid off.

6) Fill in the missing areas to help create an equation

7) Write a function rule

8) What would ( ) mean? What would the value be (include the units)?

Independent

variable

Dependent Variable

( )

Function

Notation

9) What is the domain and range of the function? Explain the limitations of the domain and the range.

Use the following financial situation to answer the following questions 10 - 15.

John is looking to rent a new apartment. He finds one that costs an initial fee of $500 and costs $650 for

each month.

10) Indicate what parts of the example is a constant, dependent variable, and independent variable.

11) Fill in the missing areas to help create an equation

12) Write a function that shows the cost of John’s rent.

13) Write a function to find the amount of money it would cost to live in the apartment for 2 years, and find

the actual cost.

14) If John wants to bring his dog, he has to pay another $45 a month. What portion of the function will

change? Write a new function for this scenario.

15) What is the domain and range of the function? Explain the limitations of the domain and the range.

Independent

variable ( ) Dependent Variable

Function

Notation

( )

Cost of

rent

HOMEWORK

Unit 3 Day 2: Modeling with Functions

Given the following functions, identify the dependent variable, independent variable, and constants.

1) ( )

2) ( ) √

3) A college student has set aside $240 for the rest of the school year to use the coin-operated laundry

facility in his dormitory. Each time he uses the machines, it costs $7.50.

4) 5)

The table shows the balance owed on an interest free loan as a function ( ) of the number

of monthly payments .

6) Identify the domain and range.

7) What is the initial amount of the loan? What is the monthly

payment? Explain how you know.

8) Write a function that models the table. Identify the independent and dependent variables.

( )

( ( ))

( )

( )

( ) ( )

( )

At the beginning of the year, Jason had $40 in his savings account. He plans to deposit $20

into his account each month. By the end of January, he will have $60, $80 by the end of

February, $100 by the end of March, and so on.

9) Write a function for the Jason’s situation.

10) Fill in the table below

11) Model Jason’s saving plan. 12) Model the situation if Jason initially

deposited $70 instead of $40.

13) What is the domain and range from question 12?

14) When will Jason have $220 using the initial investment of $40?

15) Find ( ) 16) What would ( ) represent in

terms of this problem?

( ) ( ( ))

Given the following sets, determine the following

17) {(1, 5) (5, -2) (8, 3) (7, 9)

(5, 5)} 18) {(0.1, 1.2) (3.1, -1.5) (-0.3, 0.2)}

Domain: ______________ Domain: ______________

Range: ______________ Range: ______________

Is it a function? ______________ Is it a function? ______________

19)

Domain: ______________

Range: ______________

Is it a function? ______________

NOTES

Unit 3 – Day 3: Discrete Linear Functions (O.C. 4-1)

Objectives: SWBAT represent Discrete Functions

Vocabulary~

Discrete Function-

Continuous Function-

Determine if the following graphs are continuous or discrete.

1) 2) 3)

4) A function ( ) where represents the number of people attending a banquet and ( ) represents the cost.

5) A function ( ) where represents the number of hours work at your job, and ( ) represents how much money you made that shift.

You buy a printer for $80 and then pay $15 for each ink cartridge that you use. A function relating the cost,

C (in dollars), of operation the printer to the number of cartridges used n, is ( )

6) Complete the table below 7) Graph the function.

7) Determine the following

Domain: _________________ Range: ______________ Is it a function? ______________

Dependent Variable: ______________ Independent Variable: ______________

8) What is the initial cost value of the above function?

9) Which variable would change if the price of cartridges increased by $5? How about if the printer was

$90?

10) Why is this function a discrete graph?

( ) ( ( ))

Andrea receives $40 gift card to use on iTunes. It costs her $2 per song to download her favorite jams.

11) Fill in the missing areas to help create an equation

12) Write a function relating to the value of the gift card G, to the number of songs she can download s.

13) Complete the table below 14) Graph the function.

15) Determine the following Discrete / Continuous? _________________

Domain: _________________ Range: ______________ Is it a function? ______________

Dependent Variable: ______________ Independent Variable: ______________

16) What is the initial cost value of the above function?

17) Is it possible to have G (32) = –24 ? Explain.

18) What is the limit of the domain and range for this function?

( ) ( ( ))

Balance

on the gift

card

HOMEWORK

Unit 3 Day 3: Discrete Linear Functions

For examples 1-5, determine if the following graphs are continuous or discrete.

1) 2) 3)

4) A function ( ) where represents the number of CDs you want to buy and ( ) represents

the cost.

5) Johnny charges $40 per hour for piano lessons. The function is represented

as ( ) .

6) John bought x pounds of beef for a barbeque. The price for the beef was $1.49 for the first pound and

$1.09 for each additional pound. Write an equation that shows how the cost of ground beef depends

on the number of pounds x.

A. C. ( )

B. ( ) D.

7) At the beginning of the year, Jason had $40 in his savings account. He plans to deposit $20 into his

account each month. By the end of January, he will have $60, $80 by the end of February, $100 by

the end of March, and so on. Which equation describes the amount in his savings at any given

month ( )?

A. C.

B. D.

8) A movie theater charges $8.50 for an adult ticket to an evening showing of a popular movie. To

help the local animal shelter, the theater management has agreed to reduce the price of each adult

ticket by $0.50 for every can of pet food a customer contributes to a collection barrel in the theater

lobby. Which of the following shows an equation in which ( ) represents the cost of an adult

ticket in dollars for a customer who contributes x cans of pet food?

A. ( ) C. ( )

B. ( ) D. ( )

9) The cost of food at a wedding is $150 plus $17 per person attending. Write an equation that gives the

total cost of food as a function of the number of people attending.

10) Complete the table below 11) Graph the function.

12) Determine the following Discrete / Continuous? _________________

Domain: _________________ Range: ______________ Is it a function? ______________

Dependent Variable: ______________ Independent Variable: ______________

13) Explain why the bill could never equal $1,008.50.

14) Andrea receives a $40 gift card to use a town pool. It costs her $8 per visit to swim. A function relating

the value of the gift card, v, to the number of visits, n, is 40 8v n n

a. Graph the function. Label axes and scales.

b. What is the initial value? __________________________

c. What is the difference between a given card value and

the previous card value? ___________________________

d. Identify the domain and the range of the function using set notation.

________________________________________________________

Determine if the following graphs are functions.

15) 16) 17) 18)

x (x, f(x))

20