Let .

Find the hole in the graph of y = r(x).

x=8

Step-by-step explanation:

Discontinuity of a Function

We can find some functions whose graphs cannot be plotted in one stroke. It can be a hole or a vertical asymptote or a jump. To find a possible hole in a rational function, we must set both numerator and denominator to 0 independently. If a common point is found, it's a candidate for a hole if the function could eventually be redefined as continuous.

Let's find the zeros of the numerator

Factoring

We find two solutions: x=0, x=8

Let's find the zeros of the denominator

Factoring

We find three roots: x=0, x=8, x=-8

There are two common points where the function can have holes, those are

We are not sure if those values are holes or not until we find the limits

Simplifying

Since the limit exists, the function can be redefined to cover up the hole. Now let's find the limit in x=0

Simplifying

The limit does not exist and goes to infinity, it's not a hole, thus the only hole occurs when x=8

answer is more than one

step-by-step explanation: