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4-3 Writing Functions
Warm Up
Evaluate each expression for a = 2, b = –3,
and c = 8.
1. a + 3c 26
2. ab – c –14
c+b 1
3. 1
2
4. 4c – b
35
5. ba + c
17
Holt Algebra 1
4-3 Writing Functions
Objectives
Identify independent and dependent
variables.
Write an equation in function notation and
evaluate a function for given input values.
Holt Algebra 1
4-3 Writing Functions
Vocabulary
independent variable
dependent variable
function rule
function notation
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 variables
in 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 paint
Independent: measurement of the room
Holt Algebra 1
4-3 Writing Functions
Example 2
The height of a candle decrease d centimeters
for every hour it burns.
The height of a candle depends on the number of
hours it burns.
Dependent: height of candle
Independent: time
Holt Algebra 1
4-3 Writing Functions
Example 3
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 medication
Independent: weight of animal
Holt Algebra 1
4-3 Writing Functions
Helpful Hint
There are several different ways to
describe the variables of a function.
Independent
Variable
x-values
Holt Algebra 1
Dependent
Variable
y-values
Domain
Range
Input
Output
x
f(x)
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: cost
Independent 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: cost
Independent variable: pounds
Holt Algebra 1
4-3 Writing Functions
You can think of
a function as an
input-output
machine.
input
x 2
function
f(x)=5x
30
output
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.
f(x) = 3(x) + 2
f(7) = 3(7) + 2 Substitute
7 for x.
= 21 + 2
Simplify.
= 23
Holt Algebra 1
f(x) = 3(x) + 2
f(–4) = 3(–4) + 2 Substitute
–4 for x.
Simplify.
= –12 + 2
= –10
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
g(–2) = 1.5(–2) – 5
=9–5
= –3 – 5
=4
= –8
Holt Algebra 1
4-3 Writing Functions
Example 8
For
, find h(r) when r = 600
and when r = –12.
= 202
Holt Algebra 1
= –2
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
Holt Algebra 1
h(c) = 2c – 1
h(–3) = 2(–3) – 1
=2–1
= –6 – 1
=1
= –7
4-3 Writing Functions
Example 10
For g(t) =
, find g(t) when t = –24 and
when t = 400.
= –5
Holt Algebra 1
= 101
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 people
dependent: cost
2. A moving company charges $130 for weekly
truck rental plus $1.50 per mile.
independent: miles
dependent: cost
Holt Algebra 1
4-3 Writing Functions
Lesson Summary: Part II
Evaluate each function for the given input values.
3. For g(t) =
, find g(t) when t = 20 and
when t = –12.
g(20) = 2
g(–12) = –6
4. For f(x) = 6x – 1, find f(x) when x = 3.5 and
when x = –5.
f(3.5) = 20
f(–5) = –31
Holt Algebra 1