Question

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

Answer 1

Answer:

x=2 is the vertical asymptote.

horizontal asymptote is y=0

Step-by-step explanation:

Find the vertical and horizontal asymptotes

$y=\frac{x^3}{(x-2)^4}$

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, $3$ so the horizontal asymptote is y=0

Answer 2

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