vertical line test

The vertical line test is a quick visual check: slide an imaginary vertical line across a graph, and if it ever touches the curve in two or more places at once, the graph is not a function. If every vertical line meets the graph at most once, the graph is a function.

Why it works comes straight from the definition. A vertical line is the set of all points with one fixed x-value. If that line crosses the curve twice, then that single input x has two outputs y — exactly what a function is forbidden to do. One x, two y's, no function.

The test is a yes-or-no diagnostic about the picture in front of you; it does not tell you the rule. A circle fails the test because a vertical line through its middle hits it top and bottom. A parabola opening up passes, because every vertical line meets it once.