Question

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.

Answer 1

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.

Answer 2

Answer:

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.