# Horizontal line test

In mathematics, the horizontal line test is a test used to determine if a function is injective, surjective or bijective.

Suppose there is a function f : X → Y with a graph., and you have a horizontal line of X x Y :[itex]y_0 \in Y, \{(x,y_0): x \in X\} = (X \times y_0) [itex] .

• If the function is injective, then it can be visualized as one whose graph is never intersected by any horizontal line more than once.
• Iff f is surjective any line will intersect the graph at least at one point
• iff f is bijective any line will intersect the graph at exactly one point.
 Missing imageHorizontal-test-ok.pngImage:Horizontal-test-ok.png Succeeds the test (injective) Missing imageHorizontal-test-fail.pngImage:Horizontal-test-fail.png Fail the test (not injective)

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