Horizontal Line Test

The Horizontal Line Test is used much less frequently than the vertical line test, despite the fact that they’re very similar. You’ll recall that any function passing the Vertical Line Test can only have one unique output of y for any single input of x.

Contrast that with the Horizontal Line Test, which says that no y value corresponds to two different x values. If a function passes the Horizontal Line Test, then no horizontal line will cross the graph more than once, and the graph is said to be “one-to-one.”

The first graph on the left passes the Horizontal Line Test because a horizontal line cannot intersect it more than once.

The second graph on the left does not pass the Horizontal Line Test because any horizontal line between y=1 and y=-1 would intersect it more than once.