Question

Find the vertical asymptotes of the following function:

y = x3 − 8
________
x^2 + 9

Select the appropriate response:
A) 4
B) 7
C) None

Answer 1

Answer:

Option C is the right choice.

Step-by-step explanation:

$\mathrm{Vertical\:asymptotes\:of\:}\frac{x^3-8}{x^2+9}\:\:=\:\:\mathrm{None}$

$\mathrm{Vertical\:asymptotes\:of\:rational\:Functions}:$

For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator, of the simplified function.

The given function is true for all  $x \in \mathbb{R}$  and has no undefined points.

Therefore, no vertical asymptotes.

Answer 2

Answer:

C) None

Step-by-step explanation:

Since x² + 9 = 0 has no roots, the curve has no vertical asymptotes