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Definition

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines. The motivation for the vertical line test is as follows: A relation f:A->B is a function precisely when each element x element A is matched to at most one value f(x) element B and, as a result, any vertical line in the plane can intersect the graph of a function at most once. Therefore, the vertical line test concludes that a curve in the plane represents the graph of a function if and only if no vertical line intersects it more than once.

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