Question

guided practice
you are now going to solve five problems—one for each step in the process for graphing a rational function with an infinite discontinuity. write each problem and answer in your notebook.
step 1 is to identify the vertical asymptote(s).
find the vertical asymptote(s) for $y = \frac{2}{x^2 - 9}$.
a. none
b. $x = -3$
c. $x = -3$, $x = 3$
d. $x = 3$

Explanation:

Step1: Factor denominator

Denominator $x^2 - 9 = (x-3)(x+3)$

Step2: Find undefined points

Set denominator to 0: $(x-3)(x+3)=0$ → $x=3$ or $x=-3$

Step3: Check numerator at points

Numerator=2≠0 at $x=±3$, so vertical asymptotes exist here.

Answer:

C. x=-3, x=3