Horizontal line test

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" : XY with a graph., and you have a horizontal line of X x Y :y_0 in Y, {(x,y_0): x in X} = (X imes 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 horizontal line will intersect the graph at least at one point
*If f is bijective any horizontal line will intersect the graph at exactly one point.

This test is also used to find whether or not the inverse of the function is indeed a function as well. This is due to the reflective properties of the function over y=x.


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