Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }$$
A) $x = 9$
B) $x = 7$
C) $x = 0 , x = - 7$
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 $f(x) = \frac{x - 9}{x^2 + 7x}$, setting the denominator equal to zero gives $x^2 + 7x = 0$, which factors to $x(x + 7) = 0$. This yields $x = 0$ and $x = -7$ as the points where vertical asymptotes occur.

Give the Equations of Any Vertical Asymptotes for the Graphs f(x)=x−9x2+7xf ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }f(x)=x2+7xx−9​

Give the Equations of Any Vertical Asymptotes for the Graphs $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 7 x }$