Vertical line test

{{Short description|Test to determine whether a curve is a graph of a function}}

File:Vertical line test.png shows the domain of the (to be tested) function.]]

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.

{{cite book | last = Stewart | first = James | title = Calculus: Concepts and Contexts | url = https://archive.org/details/studentsolutions00cole | url-access = registration |edition=2nd |page=[https://archive.org/details/studentsolutions00cole/page/17 17] | publisher = Brooks/Cole | location = Pacific Grove | year = 2001 | isbn = 978-0-534-37718-2 |quote=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.}}