Question

Find the vertical asymptotes and holes for the graph of the rational function.y = (x+3)(x-6)———————-(x-6)(x+1)Identify any vertical asymptotes for the graph of the function. Select all that apply.

Answer 1

The Solution:

Given:

$\frac{\left(x+3\right)\left(x-6\right)}{\left(x-6\right)\left(x+1\right)}$

We are required to find the vertical asymptote for the graph and also find the hole of the function.

Step 1:

Plot the graph of the function.

From the above graph, the vertical asymptote is x = -1

Step 2:

Find the hole of the function.

The common factor in the numerator and denominator is (x-6).

So,

$\begin{gathered} x-6=0 \\ x=6 \end{gathered}$

Thus, the hole of the function is: x = 6