In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x. If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.[1]
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Stewart, James (2001). Calculus: Concepts and Contexts (2nd ed.). Pacific Grove: Brooks/Cole. p. 17. ISBN 978-0-534-37718-2.
The Vertical Line Test: A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once.