Question

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

Answer 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