Find all vertical asymptotes of the function $y ( x ) = \frac { x - 5 } { x ^ { 2 } - 5 x + 4 }$
A) $x = 1 , x = 4$
B) $x = 1$
C) $x = 4$
D) $x = - 1 , x = 5$
E) $\text { no vertical asymptotes }$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (and the numerator is not zero at those points). Factoring the denominator: $x^2 - 5x + 4 = (x - 1)(x - 4)$. Setting each factor equal to zero gives $x = 1$ and $x = 4$, which are the points where the function is undefined and thus are the vertical asymptotes.

Find All Vertical Asymptotes of the Function y(x)=x−5x2−5x+4y ( x ) = \frac { x - 5 } { x ^ { 2 } - 5 x + 4 }y(x)=x2−5x+4x−5​

Find All Vertical Asymptotes of the Function $y ( x ) = \frac { x - 5 } { x ^ { 2 } - 5 x + 4 }$