FUNCTION NOTATION AND EVALUATING FUNCTIONS

SECTIONS 5.1 & 14.1B

A ________ is a set of __________________.relation ordered pairs

The ________ is the ______ of ________ numbers in a relation.

range

set first

The ________ is the ______ of ________ numbers in a relation.

domain

set second

A ___________ is a relation in which no number in the _________ is __________.

functiondomain repeated

Functions can be represented five different ways:

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

mapping

graph

table

Set of ordered pairs

equation

Sometimes we will only know one part of the ordered pair. We can use the equation to find the missing number.Example 1: Complete each ordered pair so that it is a solution to 2 9.x y

a. ( 1, ? )

What is ____ if _________? 1x y2 9x y 2 1 9y

2 9y -2

7y

(1, 7)

b. ( ?, 9 )

What is ____ if _________? 9y x

2 9x y

-9

2 0x

(0, 9)

2 9 9x

0x 2 2

2 4 9y

c. ( 4, ? )

What is ____ if _________? 4x y2 9x y

-8

(4, 1)

1y

8 9y

TRY THIS….

Does not mean multiplication!

Function notation replaces the independent variable, y with either f(x), g(x), or h(x).

f(x) is read as “ ____ _____ _____”

g(x) is read as “ ____ _____ _____”

h(x) is read as “ ____ _____ _____”

f of x

g of x

h of x

Instead of writing, 3y x , we replace the y with ( )f x

( ) 3f x x

is read as “ ___________________________________” of equals 3f x x

2( )f x x( )f x x

( )f x x2( ) 3f x x

Function Notation

Read as

2of equalsf x xof equals the f x absolute value of x

of equals the square root off x x2of equals 3f x x

Look at the mappings below. What is happening to each number in the domain to get the corresponding number in the range?

2

5

10

8

11

16

Domain Range

Function Rule:

-3

0

5

-6

0

10

Domain Range

Function Rule:

x ( )f x

What is happening to x to get the

corresponding f(x) value?

( ) 6f x x

x ( )f x

What is happening to x to get the

corresponding f(x) value?

( ) 2f x x

The ______________ can be thought of as an operation that changes the

numbers in the ___________ to make the ________.

function rule

domain

range

Function notation:

2( ) 3 4 2f x x x The right side of any function notation is called the _____________. function rule

6y x

22 3y x

4 7y x

Equation Function Notation Function Rule

( ) 6f x x 6x 2( ) 2 3f x x 22 3x

( ) 4 7f x x 4 7x

Replace the y with

f(x)

Right side of notation

Function Ruleoutput

input

The numbers of the domain are sometimes called the ________ and the range is called the ___________.

inputoutput

x

( )f x

Changes the domain into the range

Find the range for the function ( ) 3 1f x x if the domain of f(x) is { 0, 2, 4 }.

range

domain

3 1x

3 0 1

0

1

3 2 1

2

7

3 4 1

4

13

Range = { }1, 7, 13

Domain Range

0

2

4

1

7

13

Written as ordered pairs:

{(0,1), (2,7), (4,13)}

Try this…

For the function, 2( ) 2h x x , find the range

if the domain is { -3, 0, 4 }.2 2x

Input Output

=

=

=

3 23 2 9 2 7

0 20 2 0 2 2

4 24 2 16 2 14

Range: { 2,7,14}

Sometimes we only want to only evaluate one element of the domain.

For example, if 2( ) 3 1g x x x find ( )g x when 2x

“find ( )g x when 2x ”, can be written in a shorter form as “ (2)g ”.

Example 2: If 2( ) 3 1g x x x find (2)g

.

2( ) 3 1g x x x

232) 12( 2g

( ) 42 6 1g

( 12)g

Plug 2 into the

function rule.

(2) 1g

Try these… If 2( ) 2 3 2h x x x find:

A. (0)h. 2

0 0 20( ) 2 3h

( ) 00 0 2h

( 20)h

B. (2)h

. 22 2 22( ) 2 3h

( ) 22 4 6 2h

( ) 82 6 2h

( 02)h