Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of function in your answer.

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A function is by definition a relation that relates members of one set with members of another set by one to one correspondence. Hence, one element is solely associated to another element. The vertical line test is a conventional way to determine if a curve is a graph of a function or not. When the vertical line intersects the xy-plane at more than one point, then the expression is not a function. Otherwise, if there is only one point of intersection, then it is a function.

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