Vertical line test

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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. By failing the vertical line test, a curve that does not represent a function may be described more broadly as a multivalued function, where its multiple values are each the intersections with the vertical line. An example is the equation y 2 = x {\displaystyle y^{2}=x} , which gives y = ± x {\displaystyle y=\pm {\sqrt {x}}} when solved for y {\displaystyle y} . Here, the ± {\displaystyle \pm } symbol yields two distinct output values, failing the vertical line test on the domain right of the Y-axis.