## Functions: Vertical Line Test for Functions

The Vertical Line Test is a test to determine if a relation or its graph is a function or not. For a relation or graph to be a function, it can have at most a single y-value for each x-value. Thus, a vertical line drawn at any x-position on the graph of a function will intersect the graph at most once.

To use the vertical line test graphically, take a ruler or other "vertical line" and move it from one end of the x axis to the other. If the graph intersects the ruler or vertical line more than once at any given point, the graph is not a function. However, if the graph intersects the vertical line only once at any given point, it is a function.

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