Holt Algebra 1

4-3 Writing Functions

Warm UpEvaluate each expression for a = 2, b = –3, and c = 8. 1. a + 3c

2. ab – c

3.

12

c + b

4. 4c – b

5. ba + c

26

–14

1

35

17

Holt Algebra 1

4-3 Writing Functions

Identify independent and dependent variables.

Write an equation in function notation and evaluate a function for given input values.

Objectives

Holt Algebra 1

4-3 Writing Functions

independent variabledependent variablefunction rule function notation

Vocabulary

Holt Algebra 1

4-3 Writing Functions

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

Holt Algebra 1

4-3 Writing Functions

Directions: Identify the independent and dependent variablesin the situation.

Holt Algebra 1

4-3 Writing Functions

Example 1

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 paintIndependent: measurement of the room

Holt Algebra 1

4-3 Writing Functions

The height of a candle decrease 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 2

Holt Algebra 1

4-3 Writing Functions

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

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

Dependent: amount of medicationIndependent: weight of animal

Example 3

Holt Algebra 1

4-3 Writing Functions

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)

Holt Algebra 1

4-3 Writing Functions

Example 4

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

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

Dependent variable: costIndependent variable: time

Holt Algebra 1

4-3 Writing Functions

Example 5

Camryn buys p pounds of apples at $0.99 per pound.

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

Dependent variable: costIndependent variable: pounds

Holt Algebra 1

4-3 Writing Functions

You can think of a function as an input-output machine.

input

10

x

functionf(x)=5x

output

5x

6

30

2

Holt Algebra 1

4-3 Writing Functions

Directions: Evaluate the function for the given input values.

Holt Algebra 1

4-3 Writing Functions

Example 6

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

= 21 + 2

f(7) = 3(7) + 2 Substitute 7 for x.

f(x) = 3(x) + 2

= 23

Simplify.

f(x) = 3(x) + 2

f(–4) = 3(–4) + 2 Substitute –4 for x.Simplify.= –12 + 2

= –10

Holt Algebra 1

4-3 Writing Functions

Example 7

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

g(t) = 1.5t – 5 g(t) = 1.5t – 5

g(6) = 1.5(6) – 5

= 9 – 5

= 4

g(–2) = 1.5(–2) – 5

= –3 – 5

= –8

Holt Algebra 1

4-3 Writing Functions

Example 8

For , find h(r) when r = 600

and when r = –12.

= 202 = –2

Holt Algebra 1

4-3 Writing Functions

Example 9

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

h(c) = 2c – 1

h(1) = 2(1) – 1

= 2 – 1

= 1

h(c) = 2c – 1

h(–3) = 2(–3) – 1

= –6 – 1

= –7

Holt Algebra 1

4-3 Writing Functions

Example 10

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

when t = 400.

= –5 = 101

Holt Algebra 1

4-3 Writing Functions

Lesson Summary: Part I

Identify the independent and dependent variables.

1. A buffet charges $8.95 per person.independent: number of peopledependent: cost

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

Holt Algebra 1

4-3 Writing Functions

Lesson Summary: 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) = 20f(–5) = –31

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

when t = –12.

g(20) = 2g(–12) = –6