A function is a rule which maps each element of the domain to exactly one element in the range. A function can be described by many ways like with a mapping diagram, by a set of ordered pairs, by an equation, with function notation or with a function table. Each of this method is used depending upon the need.
A function table is a numerical representation of the function and is especially useful in describing the relationship in experimental data. Let us learn how to identify the functions represented by the function table by observing the pattern in the values, or how to write the function rule which the table represents.

When the tabulated values of two variables follow a rule, the table displaying these values is called a function table.

A function table consists of two columns one for input and another for output. The input column contains of values of the independent variable and the output column displays the corresponding values of the dependent variable. Each input value is paired exactly with one output value. This means, repetition of input values will not be seen.

Example:
Hours worked
x
(input)

Amount earned
in dollars y
(output)

20 250
25
300
30
350
35
400
40
450

In the above table, the input column consists of values of the independent variable x and the corresponding values of the dependent variable y are shown in the output column. This table describes y as a linear function of x.