Find the asymptote(s) of the given function.
-$f ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x }$ vertical asymptotes(s)
A) $x = 6$
B) $x = 0 , x = - 6$
C) $x = - 6$
D) $x = 7$

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is equal to zero, as long as the numerator is not also zero at those points. For $f(x) = \frac{x - 7}{x^2 + 6x}$, setting the denominator equal to zero gives $x^2 + 6x = 0$, which factors to $x(x + 6) = 0$. This yields $x = 0$ and $x = -6$ as the points where the function is undefined, indicating vertical asymptotes at $x = 0$ and $x = -6$.

Find the Asymptote(s) of the Given Function f(x)=x−7x2+6xf ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x }f(x)=x2+6xx−7​

Find the Asymptote(s) of the Given Function $f ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x }$