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.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.Compare your response to the sample response above. What did your explanation include?It describes a vertical line passing through the graph more than once.It refers back to the definition of a function.

Answer 1

The key things to remember about a function is this: one input, one output.

The input must be in the domain of the function. The domain is the set of allowed inputs (eg: you must avoid dividing by zero).

If an input like x = 4 leads to simultaneous outputs of y = 1 and y = 5 at the same time, then we don't have a function. Visually this leads to the graph failing the vertical line test. A single straight line cannot pass through more than one point on the curve.

So if it is impossible to have a single straight line pass through more than one point on the curve, then that curve is a function.