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    Inverse Functions: Horizontal Line Test for Invertibility


    A function f  is invertible if and only if no horizontal straight line intersects its graph more than once.

    Example #1:

     Use the Horizontal Line Test to determine whether or not the function y = x2 graphed below is invertible.



    Solution #1:
    For the first graph of y = x2, any line drawn above the origin will intersect the graph of f  twice.  Therefore, f  is not invertible.


    Example #2    :

     Use the Horizontal Line Test to determine whether or not the function y = x3 graphed below is invertible.



    Solution #2:

    For the first graph of y = x3, no horizontal line intersects graph of f  more than once. Therefore, f  is invertible.


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