Determine the equations of the vertical and horizontal asymptotes, if any, for g (x) = x^3 / (x-2) (x+1)

a. x=2, x-1

b. x=-2, y=-1

c. x=-2, x=-1

d. x=2, y=-1

For this case what we should see are the values for which the function is not defined.

So we have to study your domain:

g (x) = x ^ 3 / (x-2) (x + 1)

We see what values make the denominator is not defined:

(x-2) (x + 1) = 0

First value:

x-2 = 0

x = 2

Second value:

x + 1 = 0

x = - 1

The function has two vertical asymptotes:

x = 2

x = - 1

Answer:

a. x = 2, x-1