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$y$ is a function of $x$or that

$y$ depends on $x.$

$y=f(x)$

Note that every function is a relation, but not every relation is a function. In the following applet, three different relations are analyzed to determine whether they are functions.

In Relation III, although one of the outputs corresponds to two different inputs, it is still a function because each input has exactly one output. Depending on how a relation is represented, there are different methods to determine whether or not it is a function.

Determining Whether a Relation Is a Function | |
---|---|

If represented as | Use |

a set of coordinates or a table of values | a mapping diagram |

a graph in the coordinate plane | the vertical line test |