1.1: Four Ways To Represent A Function - Mathematics LibreTexts

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Example \(\PageIndex{5}\): Identifying Tables that Represent Functions

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

Table \(\PageIndex{6}\)
Input Output
2 1
5 3
8 6
Table \(\PageIndex{7}\)
Input Output
-3 5
0 1
4 5
Table \(\PageIndex{8}\)
Input Output
1 0
5 2
5 4

Solution

Table \(\PageIndex{6}\) and Table \(\PageIndex{7}\) define functions. In both, each input value corresponds to exactly one output value. Table \(\PageIndex{8}\) 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 \(\PageIndex{6}\) can be represented by writing

\[f(2)=1\text{, }f(5)=3\text{, and }f(8)=6 \nonumber\]

Similarly, the statements

\[g(−3)=5\text{, }g(0)=1\text{, and }g(4)=5 \nonumber\]

represent the function in Table \(\PageIndex{7}\).

Table \(\PageIndex{8}\) cannot be expressed in a similar way because it does not represent a function.

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