explain why a graph that fails the vertical - line test does not represent a function. be sure to use the…

Brief Explanations:

A function is defined as a relation where each input (x - value) has exactly one output (y - value). The vertical - line test checks this. If a vertical line intersects a graph at more than one point, it means that for a single x - value, there are multiple y - values. This violates the definition of a function.

Answer:

A graph that fails the vertical - line test does not represent a function because the vertical - line test checks if for every x - value there is exactly one y - value. When a vertical line intersects the graph at more than one point, there are multiple y - values for a single x - value, which goes against the definition of a function.