How Do You Tell If a Relation Is a Function?

In math, it can be determined if a relation is a function through the vertical line test. This test must be performed on a function that has been graphed.

Once a relation has been graphed, the vertical line test can be used to determine if the relation is a true function. To perform the vertical line test, take a pencil or pen and lie it vertically at the start of the graph. Next, move this vertically positioned pencil in a horizontal line from the beginning of the graph to the end. If the pencil only ever touches one point on the graph at one time, then the relation is a function. This test works because a function is a relation in which every x-point only has one y-point.