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4.3 WRITING FUNCTIONS
Objectives
Identify independent and dependent variables.
Write an equation in function notation and evaluate a
function for given input values.
Vocabulary
independent variable
dependent variable
function rule
function notation
Example 1: Using a Table to Write an Equation
Determine a relationship between the x- and y-values. Write an equation.
x
5
10
15
20
y
1
2
3
4
How do we go from 5 to 1?
method works for all x and y?
Equation
Does equation represent a function?
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.
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.
What are our two variables? Then complete the sentence:
The
depends on the
Dependent:
Independent:
The height of a candle decrease d centimeters for every hour it burns.
Helpful Hint
There are several different ways to describe the variables of a function.
Independent
Variable
Dependent
Variable
x-values
y-values
Domain
Range
Input
Output
x
f(x)
The dependent variable is a function of the independent variable.
y
is
y
=
a function of
f
x.
(x)
y = f(x)
An algebraic expression that defines a function is a function rule.
Example 3A: Writing Functions
Identify the independent and dependent variables. Write a rule in function
notation for the situation.
A math tutor charges $35 per hour.
Variables?
Dependent:
Independent:
The
depends on
Let h represent the number of hours of tutoring.
The function rule for the amount a math tutor charges is f(h) = 35h.
You can think of a function as an input-output machine.
What is the machine doing to the inputs?
input
x
2
Example 4A: Evaluating Functions
Evaluate the function for the given input values.
For f(x) = 3x + 2, find f(7) and f(-4).
function
f(x)=5x
f(x) = 3(x) + 2
f(7) = 3(7) + 2
= 21 + 2
= 23
Substitute
7 for x.
Simplify.
f(–4) =
30
output
Example 5: Finding the Reasonable Range and Domain of a Function
Joe has enough money to buy 1, 2, or 3 DVDs at $15.00 each.
Write a function to describe the situation. Find a reasonable domain and range
of the function.
How many DVDs will Joe buy?
So what are our variable?
Money spent
f(x)
is
=
$15.00
$15.00
for each
•
DVD.
x
If Joe buys x DVDs, he will spend f(x) = 15x dollars.
Joe only has enough money to purchase 1, 2, or 3 DVDs. A reasonable
domain is {1, 2, 3}.
Could 1.5 be one of the x-values in the domain?
What is the range?
1
3
2
x
f(x)
15(1) = 15
15(2) = 30
15(3) = 45