Question

Which of the following are vertical asymptotes of the function?
f(x)= 3(x-1(x+2)(x+3)/(x-1)^2(x+2)(x-3)(x-4)
Select all that apply

x = 1

x = –2

x = 3

x = 4

Answer 1

First simplify:

f(x) = 3(x-1)(x+2)(x+3) / [(x-1)^2(x+2)(x-3)(x-4)]
Cancel common factors (x-1) and (x+2):

f(x) = 3(x+3) / [(x-1)(x-3)(x-4)]

Vertical asymptotes occur where a nonremovable factor remains in the denominator. After simplification the denominator has factors (x-1), (x-3), (x-4), so vertical asymptotes are at

x = 1, x = 3, x = 4.

x = −2 is a removable hole (factor canceled), not a vertical asymptote.