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.

Sample Response: If a vertical line intersects a graph more than once, then the graph has more than one y-value for a given x-value. You can't have two y-values for an x-value in a function. Therefore, the graph is not a function.