A close look at zeros of rational functions

Topic:
Functions

Plot a rational function with a zero at x=1.

If is a rational function with a zero at , what can you conclude?

The converse, however, is not true. That is, if is a rational function with , it is not necessarily the case that has a zero at . Plot an example of such a rational function below.
Plot a rational function below such that , and 's only zero occurs at .

Correctly complete the claim below

is a zero of the rational function if and only if: