Example 5 from Algebra and Trigonometry, 3.1 Functions and Function Notation

Identifying Tables that Represent Functions

Which table, Table 6, Table 7, or Table 8, represents a function (if any)?

Input	Output
2	1
5	3
8	6

Table 6

Input	Output
–3	5
0	1
4	5

Table 7

Input	Output
1	0
5	2
5	4

Table 8

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Table 6 and Table 7 define functions. In both, each input value corresponds to exactly one output value. Table 8 does not define a function because the input value of 5 corresponds to two different output values.

When a table represents a function, corresponding input and output values can also be specified using function notation.

The function represented by Table 6 can be represented by writing

$f (2) = 1, f (5) = 3, and f (8) = 6$
Similarly, the statements

$g (- 3) = 5, g (0) = 1, and g (4) = 5$
represent the function in Table 7.

Table 8 cannot be expressed in a similar way because it does not represent a function.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Does Table 9 represent a function?

Input	Output
1	10
2	100
3	1000

Table 9

How did it go?