Article · Wikipedia archive · Last revised Jul 4, 2026

Vertical line test

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.

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The vertical line test, shown graphically. The abscissa shows the domain of the (to be tested) function. source ↗

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

See also

See also

Notes

Notes

  1. 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.