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.
Vocabulary
independent variable
dependent variable
function rule
function notation

2. 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
How do we go from 5 to 1?
method works for all x and y?
Equation
Does equation represent a function?

3. Example 2A: Identifying Independent and Dependent Variables
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.

4. 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 a function of x.
y = f(x)
y = f (x)
An algebraic expression that defines a function is a function rule.

5. 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.

6. Example 4A: Evaluating Functions
input
You can think of a function as an input-output machine. x 2
What is the machine doing to the inputs? 6
Example 4A: Evaluating Functions
function
f(x)=5x
Evaluate the function for the given input values.
For f(x) = 3x + 2, find f(7) and f(-4).
f(x) = 3(x) + 2 5x
Substitute
7 for x.
f(7) = 3(7) + 2 10
f(–4) = 30
output =
Simplify.
= 23

7. 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
is $ for each DVD.
f(x) = $ • 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? x 1 2 3
f(x)
15(1) = 15
15(2) = 30
15(3) = 45