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 :

y_0 \in Y, \{(x,y_0): x \in X\} = (X \times y_0)

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.

Succeeds the test (injective)

Fail the test (not injective)

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