Find the asymptote(s) of the given function.
-$f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 }$ vertical asymptotes(s)
A) None
B) $x = - 1$
C) $x = 1$
D) $x = 2 , x = - 2$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero, as long as the numerator is not also zero at those points. For $f(x) = \frac{x - 4}{x^2 + 1}$, the denominator $x^2 + 1$ is never zero for any real value of $x$ because $x^2$ is always non-negative, making $x^2 + 1$ always positive. Therefore, there are no vertical asymptotes.

Find the Asymptote(s) of the Given Function f(x)=x−4x2+1f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 }f(x)=x2+1x−4​

Find the Asymptote(s) of the Given Function $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 }$