Vertical Line Test

Recall that a function is a correspondence between two sets, say X and Y, that assigns to each element x of X exactly one element y of Y. This definition specifies that each x can only be paired with exactly one y.

Thus, if a graph contains points whose first coordinates are paired with two or more different second coordinates, the graph cannot represent a function.

Note that points with the same first coordinates in a given graph are contained on a single vertical line. If any vertical line intersects a graph at more than one point, there are at least two different ordered pairs with the same first coordinates. This means that the graph is not a graph of a function. You now have a method of determining whether or not a graph represents a function. Such method is called the vertical line test. Refer to the example on the next page to learn how to do the vertical line test.