Question

Explain the circumstances under which the graph of a rational function will have a hole.

Short answer

A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.

Step-by-step solution

Step 1. Definition and explanation. 

A rational function is any function that can be written as the ratio of two polynomial functions or as $\frac{p}{q};q\ne 0$.

A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.

At this point the value of the function is undefined.