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