Intermediate Algebra (11th edition)

Evaluating a Function

Let Find the value of the function ƒ for

Replace xwith 2.

Multiply.

ƒ 122 = 13 Add.

ƒ 122 = 18 - 5

ƒ 122 = 9 # 2 - 5

ƒ 1 x 2 = 9 x- 5

ƒ 1 x 2 = 9 x-5. x=2.

EXAMPLE 1

190 CHAPTER 3 Graphs, Linear Equations, and Functions

OBJECTIVES OBJECTIVE 1 Use function notation. When a function ƒ is defined with a rule

or an equation using xand yfor the independent and dependent variables, we say,

“y is a function of x” to emphasize that y depends on x. We use the notation

yƒ 1 x 2 ,

Function Notation and Linear Functions

3.6

1 Use function

notation.

2 Graph linear and

constant functions.

NOW TRY
EXERCISE 1
Let Find the
value of the function ƒ for
x=-2.

ƒ 1 x 2 = 4 x+3.

called function notation,to express this and read as “ƒ ofx.”The letter ƒ is a

name for this particular function. For example, if we can name this

function ƒ and write

ƒ 1 x 2 = 9 x-5.

y= 9 x- 5,

ƒ 1 x 2

The parentheses

here do notindicate

multiplication.

ƒ is the name of the function.

xis a value from the domain.

is the function value (or y-value)

that corresponds to x.

ƒ 1 x 2

is just another name for the dependent variable y.

We can evaluate a function at different values of xby substituting x-values from

the domain into the function.

ƒ 1 x 2

Thus, for , the corresponding function value (or y-value) is 13. is

an abbreviation for the statement “If in the function ƒ, then ” and is

represented by the ordered pair 12 , 132.

x= 2 y= 13

x= 2 ƒ 122 = 13

Read as “ƒ of 2”

or “ƒ at 2.”

ƒ 122

CAUTION The symbol does notindicate “ƒ times x,” but represents the

y-value associated with the indicated x-value. As just shown, is the y-value that

corresponds to the x-value 2 in the function.

ƒ 122

ƒ 1 x 2

These ideas can be illustrated as follows.

Name of the function

Defining expression

Value of the function Name of the independent variable

y = ƒ 1 x 2 = 9 x- 5

NOW TRY ANSWER

1. 
   
   
   
   • 5
   
   
   
   

NOW TRY