Question

Determine the equations of the vertical and horizontal asymptotes, if any, for y=x^3/(x-2)^4

A. x=2, y=0
B. x=2
C. x=2, x=-2
D. x=2, y=1

Answer 1

The answer is A. Just took the test and got it right. 

Answer 2

x=2 is the vertical asymptote.

horizontal asymptote is y=0

Explanation:

Find the vertical and horizontal asymptotes

`y=(x^3)/((x-2)^4)`

To find out the vertical asymptote, we set the denominator =0 and solve for x

`(x-2)^4=0`

Take fourth root on both sides

`x-2=0`

Add 2 on both sides , so x=2 is the vertical asymptote.

To find horizontal asymptote , we look at the degree of both numerator and denominator

Degree of numerator is 3 and the degree of denominator is 4

When the degree of numerator is less than the degree of numerator then horizontal asymptote is y=0

Here,
`3 <4` so the horizontal asymptote is y=0