# 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.^{[1]}

To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the *y*-axis for any chosen value of *x*. If the vertical line you drew intersects the graph more than once for any value of *x* then the graph is not the graph of a function. If, alternatively, a vertical line intersects the graph no more than once, no matter where the vertical line is placed, then the graph is the graph of a function. For example, a curve which is any straight line other than a vertical line will be the graph of a function. As another example, a sideways parabola (one whose directrix is a vertical line) is not the graph of a function because some vertical lines will intersect the parabola twice.

## See also

## Notes

- ↑ 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.