Question

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.

Answer 1

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.

Answer 2

If vertical-line test fails it means it is giving more than one value of y which does not satisfy the definition of a function.

Explanation:

If a mapping is like
`f:A\rightarrow B` is said to be a function if for different values of x we get different values of y

So, if a vertical line test fails does not represents a function because from vertical line test we get the values of y

So, if vertical line intersect the graph at more than one point say two points it means vertical test fails because it will give two values of y.