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

Respuesta :

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