3-3 Writing Functions - Quia McDougal Algebra 1 3-3 Writing Functions Example 1: Using a Table to...

Holt McDougal Algebra 1

3-3 Writing Functions

Example 1: Using a Table to Write an Equation

Determine a relationship between the x- and y-values. Write an equation.

x

y

5 10 15 20

1 2 3 4

Step 1 List possible relationships between the first x or y-values.

5 – 4 = 1 or



Check It Out! Example 1

Determine a relationship between the x- and y-values. Write an equation.

{(1, 3), (2, 6), (3, 9), (4, 12)}

x

y

1 2 3 4

3 6 9 12



The equation in Example 1 describes a function because for each x-value (input), there is only one y-value (output).



The input of a function is the independent variable. The output of a function is thedependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.



Example 2A: Identifying Independent and

Dependent Variables

Identify the independent and dependent variables

in the situation.

A painter must measure a room before deciding how much paint to buy.

The amount of paint depends on the measurement of a room.

Dependent: amount of paint

Independent: measurement of the room




in the situation.

The height of a candle decreases d centimeters for every hour it burns.

Dependent: height of candle

Independent: time

The height of a candle depends on the number of hours it burns.

Example 2B: Identifying Independent and

Dependent Variables



A veterinarian must weigh an animal before determining the amount of medication.

The amount of medication depends on the weight of an animal.

Dependent: amount of medication

Independent: weight of animal


in the situation.

Example 2C: Identifying Independent and

Dependent Variables



Helpful Hint

There are several different ways to describe the variables of a function.

IndependentVariable

DependentVariable

x-values y-values

Domain Range

Input Output

x f(x)



Check It Out! Example 2a

A company charges $10 per hour to rent a jackhammer.

Identify the independent and dependent variable in the situation.

The cost to rent a jackhammer depends onthe length of time it is rented.

Dependent variable: cost

Independent variable: time



Identify the independent and dependent variable in the situation.

Check It Out! Example 2b

Apples cost $0.99 per pound.

The cost of apples depends on the number of pounds bought.

Dependent variable: cost

Independent variable: pounds



An algebraic expression that defines a function is a function rule. Suppose Tasha earns $5 for each hour she baby-sits. Then 5 • x is a function rule that models her earnings.

If x is the independent variable and y is the dependent variable, then function notation for yis f(x), read “f of x,” where f names the function.

When an equation in two variables describes a function, you can use function notation to write it.



The dependent variable is a function of the independent variable.

y is a function of x.

y = f (x)

y = f(x)



Identify the independent and dependent variables. Write an equation in function notation for the situation.

A math tutor charges $35 per hour.

The function for the amount a math tutor charges isf(h) = 35h.

Example 3A: Writing Functions

The fee a math tutor charges depends on number of hours.

Dependent: fee

Independent: hours

Let h represent the number of hours of tutoring.



A fitness center charges a $100 initiation fee plus $40 per month.

The function for the amount the fitness center charges is f(m) = 40m + 100.

Example 3B: Writing Functions


The total cost depends on the number of months, plus $100.

Dependent: total cost

Independent: number of months

Let m represent the number of months





Steven buys lettuce that costs $1.69/lb.

The function for the total cost of the lettuce is f(x) = 1.69x.

The total cost depends on how many pounds of lettuce Steven buys.


Independent: pounds

Let x represent the number of pounds Steven buys.





An amusement park charges a $6.00 parking fee plus $29.99 per person.

The function for the total park cost is

f(x) = 29.99x + 6.

The total cost depends on the number of persons in the car, plus $6.


Independent: number of persons in the car

Let x represent the number of persons in the car.



You can think of a function as an input-outputmachine. For Tosha’s earnings, f(x) = 5x. If you input a value x, the output is 5x.

input

x

function

f(x)=5x

output30

2



Example 4A: Evaluating Functions

Evaluate the function for the given input values.

For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.

f(7)= {23} = f(-4)={–10}



Example 4B: Evaluating Functions


For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

g(6)= {4} g(t)= {–8}



Example 4C: Evaluating Functions


For , find h(r) when r = 600

and when r = –12.

h(r)= {202} h(r)= {–2}





For h(c) = 2c – 1, find h(c) when c = 1 and when c = –3.

h(1)= {1} h(-3)= {–7}





For g(t) = , find g(t) when t = –24 and

when t = 400.

g(-24)= {–5} g(400)= {101}



If f(x)=6x+1 and g(x)=-2x-7, find h(x)=f(x)+g(x)

h(x)= 4x-6



Find the value of x so that the function has the given value.

1.h(x)=13x-4; -43

2.f(x)=-4x+3; 18



Find the inverse function of

f(x)=3x+7







Warm-upSimplify.

1. 𝟗

2.3𝟖

3. −𝟒( 𝟔𝟒)

In your notes, find the inverse of the function.

𝒇 𝒙 =𝟏

𝟑𝒙 − 𝟕



When a function describes a real-world situation, every real number is not always reasonable for the domain and range. For example, a number representing the length of an object cannot be negative, and only whole numbers can represent a number of people.



Example 5: Finding the Reasonable Domain and

Range of a Function

Write a function to describe the situation. Find the reasonable domain and range of the function.

Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each, if he buys any at all.

Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable domain is {0, 1, 2, 3}.

A reasonable range for this situation is {$0, $15, $30, $45}.



Check It Out! Example 5

The settings on a space heater are the whole numbers from 0 to 3. The total number of watts used for each setting is 500 times the setting number. Write a function to describe the number of watts used for each setting. Find the reasonable domain and range for the function.

For each setting, the number of watts is f(x) = 500x watts.

There are 4 possible settings 0, 1, 2, and 3, so a reasonable domain would be {0, 1, 2, 3}.

The reasonable range for this situation is {0, 500, 1,000, 1,500} watts.





Lesson Quiz: Part I

Identify the independent and dependent variables. Write an equation in function notation for each situation.

1. A buffet charges $8.95 per person.

independent: number of peopledependent: costf(p) = 8.95p

2. A moving company charges $130 for weekly truck rental plus $1.50 per mile.

independent: milesdependent: cost

f(m) = 130 + 1.50m



Lesson Quiz: Part II

Evaluate each function for the given input values.

4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5.

f(3.5) = {20}

f(–5) = {–31}

3. For g(t) = , find g(t) when t = 20 and

when t = –12.

g(20) = {2}

g(–12) = {–6}





Lesson Quiz: Part III

Write a function to describe the situation. Find the reasonable domain and range for the function.

5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour.

f(h) = 200h + 100

Domain: {0, 2, 3, 4}Range: {$0, $500, $700, $900}





























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