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The Vertical and Horizontal Line Tests for Graphs

To determine whether y is a function of x, given a graph of a relation, use the following criterion: if every vertical line you can draw goes through only 1 point, y is a function of x. If you can draw a vertical line that goes through 2 points, y is not a function of x. This is called the vertical line test.


Example 1: In the following graph, y is a function of x:

Passes Vertical Line Test


Example 2: In the following graph, y is not a function of x:


Fails Vertical Line Test

To determine whether x is a function of y, given a graph of a relation, use the following criterion: If every horizontal line you can draw passes through only 1 point, x is a function of y. If you can draw a horizontal line that passes through 2 points, x is not a function of y. This is called the horizontal line test.


Example 1: In the following graph, x is a function of y:


Passes Horizontal Line Test


Example 2: In the following graph, x is not a function of y:


Fails Horizontal Line Test

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