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

C) None

Explanation:

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

Answer 2

Option C is the right choice.

Explanation:

`\mathrm{Vertical\:asymptotes\:of\:}(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.