Question

True or False.

The graph of a rational function sometimes

has a hole.

Short answer

The given statement istrue.

Step-by-step solution

Step 1 Sometimes rational function which is of the form pqwhere q≠0 and q has some factors which are divisible by the numerators.

Consider an example,$f\left(x\right)=\frac{x^2-2x-3}{x^2-9}$.

Let us factor it.

$f\left(x\right)=\frac{\left(x+1\right)\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}$.

Step 2 Now look at the example.

In the example,$\left(x-3\right)$is the factor and $x=3$is the hole of this rational polynomial.

This means that on the graph of this function, this point will not exist and we will have to represent that with a hole on the graph.

Therefore, sometimes rational function have a hole.