Find the vertical asymptotes, if any, of the graph of the rational function.
-$$\frac { x - 49 } { x ^ { 2 } - 12 x + 32 }$$
A) $x = 4 , x = 8$
B) $x = - 4 , x = - 8$
C) $x = 4 , x = 8 , x = - 49$
D) $x = - 49$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is equal to zero, as long as those points do not also make the numerator zero (which would indicate a hole instead). For the given function, $\frac{x - 49}{x^2 - 12x + 32}$, we find the vertical asymptotes by setting the denominator equal to zero and solving for $x$. The denominator is $x^2 - 12x + 32$, which factors to $(x - 4)(x - 8) = 0$. Thus, $x = 4$ and $x = 8$ are the vertical asymptotes, making choice A correct.

Find the Vertical Asymptotes, If Any, of the Graph of the Rational