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

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Answer 2

Well you'll need to understand the definition of a function to begin with.

A function in simple terms is defined as a tool that maps to every input (x value) one unique output (y-value). If at any point, there is at least one value of x that has more than one value of y associated with it, it is not a function.

An analogy would be thinking of a function as a matchmaking tool that assigns every man (input) one particular marriage partner. If this tool finds two or more spouses for any particular man, then it is not a function.

So in short, a function maps to every x only one y.
If any x has more than one y, then it is not a function. Think about what a vertical line is and how it interacts with functions compared to non-functions.

Answer 3

If a graph fails the vertical line test, that would mean that it has more than one y-value for an x-value. If an x-value has more than one y-value, it isn't a function.