$\text { Find all vertical asymptotes (if any) of the function } f ( x ) = \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 3 } - 4 x ^ { 2 } - x + 4 } \text {. }$
A) $x = 4,1$
B) $x = 4,1 , - 1$
C) $x = - 4 , - 1$
D) $x = 1$
E) $x = - 1$

Question

$\text { Find all vertical asymptotes (if any) of the function } f ( x ) = \frac { x ^ { 2 } + 4 x + 3 } { x ^ { 3 } - 4 x ^ { 2 } - x + 4 } \text {. }$ 
A) $x = 4,1$
B) $x = 4,1 , - 1$
C) $x = - 4 , - 1$
D) $x = 1$
E) $x = - 1$

Quizplus · Accepted Answer

The denominator of the function is $x^3-4x^2-x+4=(x-4)(x+1)(x-1)$. So, the vertical asymptotes are $x=4,1,-1$.

A) x=4,1x = 4,1x=4,1 B) x=4,1,−1x = 4,1 , - 1x=4,1,−1

A) $x = 4,1$ B) $x = 4,1 , - 1$