The document provides examples and practice problems for identifying functions from tables and graphs. It includes: 1) An example of identifying a function from a pairing/table by checking if each input has a single output. 2) An example showing how to make a table and identify the range for the function y=2x. 3) An example graphing a function represented by a table of years and number of votes cast in US presidential elections. 4) A practice problem similarly graphing number of votes cast since 1972 when 18-year olds gained the right to vote. The document provides guidance, examples, and practice identifying and representing functions from tables and graphs.

1. EXAMPLE 2 Identify a function
Tell whether the pairing is a function.
a.
The pairing is not a function because the input 0 is
paired with both 2 and 3.

2. EXAMPLE 2 Identify a function
b.
Input Output
0 0
1 2
4 8
6 12
The pairing is a function because each input is paired
with exactly one output.

3. EXAMPLE 3 Make a table for a function
The domain of the function y = 2x is 0, 2, 5, 7, and 8.
Make a table for the function, then identify the range
of the function.
SOLUTION
x 0 2 5 7 8
y = 2x 2 0 = 0 2 2 = 4 2 5 = 10 2 7 = 14 2 8 = 16
The range of the function is 0, 4, 10, 14, and 16.

4. • y =2x – 3
Input Output
4
2
0
-2

5. • y = 2x – 3
Input Output
4 5
2 1
0 -3
-2 -7

6. • Graph the function y = -1/2x + 1
when the domain is -4, -2, 0, 2, 4

7. y = -1/2x + 1
x y
-4
-2
0
2
4

8. EXAMPLE 4 Graph a function represented by a table
VOTING
In 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.

9. EXAMPLE 4 Graph a function represented by a table
Years before or –12 –8 –4 0 4 8 12
since 1920
Votes (millions) 15 15 19 27 29 37 40
a. Explain how you know that the table represents a
function.
b. Graph the function represented by the table.
c. Describe any trend in the number of votes cast.

10. EXAMPLE 4 Graph a function represented by a table
SOLUTION
a. The table represents a function because
each input has exactly one output.
b. 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).
The graph of the function is shown.

11. GUIDED PRACTICE for Example 4
VOTING
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.
Years before or –12 –8 –4 0 4 8 12
since 1972
Votes (millions) 69 71 73 78 82 87 93

12. GUIDED PRACTICE for Example 4
a. Explain how you know the graph represents a
function.
ANSWER
The table represents a function because each
input has exactly one output.

13. GUIDED PRACTICE for Example 4
b. Graph the function represented by the table.
ANSWER

14. GUIDED PRACTICE for Example 4
c. Describe any trend in the number of votes cast.
ANSWER
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.

15. • Graphing functions
Assignment: P. 210 (#24-26, 28, 36, 37)
• You will need graph paper