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

A function is defined as a relation in which  each element of a given set (the domain of the function) is associated with an element of another set ( the range of the function).

Note that it is ' an element' in the second set  NOT more than one element.

If a graph fails the vertical line test ( the line passes through the graph more than once) it means that there is more than one element in the range  associated with the element in the domain - so it is not a function.