Tell whether the pairing is a function.

Identify a functionEXAMPLE 2

a.

The pairing is not a function because the input 0 is paired with both 2 and 3.

b.

Identify a functionEXAMPLE 2

OutputInput

21

0 0

4 8

6 12

The pairing is a function because each input is pairedwith exactly one output.

The range of the function is 0, 4, 10, 14, and 16.

Make a table for a functionEXAMPLE 3

of the function. function, then identify the rangeMake a table for the

2x is 0, 2, 5, 7, and 8. The domain of the function y =

x

y

2 5 70 8

= 2x 2 2 = 4 2 5 =10 2 7 =14 2 8 =162 0 = 0

SOLUTION

• y =2x – 3

Input Output

4

2

0

-2

• y = 2x – 3

Input Output

4 5

2 1

0 -3

-2 -7

• Graph the function y = -1/2x + 1

when the domain is -4, -2, 0, 2, 4

y = -1/2x + 1

x y

-4

-2

0

2

4

Graph a function represented by a table

EXAMPLE 4

VOTINGIn 1920 the ratification of the 19th amendment to the United States Constitution gave women the right to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since women were able to vote.

Graph a function represented by a tableEXAMPLE 4

Explain how you know that the table represents a function.

a.

Graph the function represented by the table.b.

Describe any trend in the number of votes cast.c.

Years before orsince 1920

–12 –8 –4 0 4 8 12

Votes (millions) 15 15 19 27 29 37 40

Graph a function represented by a table

EXAMPLE 4

SOLUTION

The table represents a function because each input has exactly one output.

a.

To graph the function, let x be the number of years before or since 1920. Let y be the number of votes cast (in millions).

b.

The graph of the function is shown.

GUIDED PRACTICE for Example 4

8. The presidential election in 1972 was the first election in which 18-year-olds were allowed to vote. The table shows the number (to the nearest million) of votes cast in presidential elections both before and since 1972.

VOTING

Years before orsince 1972

–12 –8 –4 0 4 8 12

Votes (millions) 69 71 73 78 82 87 93

GUIDED PRACTICE for Example 4

a. Explain how you know the graph represents a function.

The table represents a function because each input has exactly one output.

ANSWER

GUIDED PRACTICE for Example 4

b. Graph the function represented by the table.

ANSWER

GUIDED PRACTICE for Example 4

c. Describe any trend in the number of votes cast.

Sample answer: Before 1972, the number of votes cast increased by 2 million every 4 years. In 1972, the number increased by 5 million and continued to increase by more than 2 million every four years since 1972.

ANSWER

• Graphing functionsAssignment: P. 210 (#24-26, 28, 36, 37)

• You will need graph paper