A relation can be represented in various ways, of which a few are shown here. When a relation is given as a set of coordinates, such as $\{(0,1),$ $(\text{-}1,8),$ $(2,4)\},$ the $x$-coordinates represent the inputs, and the $y$-coordinates represent the corresponding outputs. In this example, the input $0$ is paired — or mapped — to the output $1,$ the input $\text{-}1$ is mapped to the output $8,$ and the input $2$ is mapped to the output $4.$ A table where one row gives the input and another row gives the output, is a representation of a relation.

Input ($x$)	$\text{-}2$	$1$	$5$
Output ($y$)	$3$	$2$	$1$

The relation given by the above table is the same as $\{(\text{-}2,3),$ $(1,2),$ $(5,1)\}.$

Instead of listing the set of coordinates, they can be plotted in a coordinate plane. The $x$-coordinates are the inputs, and the $y$-coordinates are the corresponding outputs.

The graph visualizes $\{(\text{-}3,\text{-}2),$ $(1,\text{-}1),$ $(1,3),$ $(4,\text{-}1)\}.$

A mapping diagram is a diagram that lists the inputs in one column, and the outputs in another column. Arrows are used to indicate which outputs correspond to which inputs.

This mapping diagram shows $\{(\text{-}2,\text{-}2),$ $(\text{-}1,0),$ $(0,2),$ $(2,\text{-}2)\}.$

The relation between inputs and outputs can also be defined using a rule. One such rule is Replacing $x$ with any input gives the value of the corresponding output, $y.$ For instance, the input $x=1$ yields the output $y=3.$ Thus, this relation maps the input $1$ to the output $3.$