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    Vertical Line Test for Functions

    A method to distinguish functions from relations

    The Vertical Line Test
    The vertical Line test is a wy to determine whether or not a relation is a function. The vertical line test simply states that if a vertical line intersects the relation's graph in more than one place, then the relation is a NOT a function.

    If you think about it, the vertical line test is simply a restatement of the the definition of a function which states that every x value must  have a unique y value. Well, if any particular x value has more than one y value, then you can pass a vertical line will intersect with the graph of the relation more than once. Let's re-examine the two relations from above:

     

    On the left are the graphs of the two relations examined above.  Relation #2 does not pass the vertical line test.

     

    Draw Vertical Line
    Practice Problems
    Problem One

     


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