To test for functions, we need to make sure that there’s only one y-value for every x-value. Visually, when you look at the graph of a relation, you can see whether every x-value is related to only one y-value by using the Vertical Line Test: Any (and every possible) vertical line may intersect with (cross) the graph at most once. We say “at most once,” because even if the relation is a function, the vertical line that crosses the x-axis at any number x that isn’t in the domain of the function won’t intersect the graph of the function at all. If some vertical line crosses the graph more than once, then the graph has failed the Vertical Line Test and the relation isn’t a function.

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