Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }$$
A) $y = 3 , y = - 7$
B) $x = 3 , x = - 7$
C) $y = 6$
D) $x = - 3 , x = 7$

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 $x^2 + 4x - 21 = (x + 7)(x - 3)$, we find the roots $x = -7$ and $x = 3$, which are the x-values where the function has vertical asymptotes.

Give the Equations of Any Vertical Asymptotes for the Graphs f(x)=6x3+5x−9x2+4x−21f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }f(x)=x2+4x−216x3+5x−9​

Give the Equations of Any Vertical Asymptotes for the Graphs $f ( x ) = \frac { 6 x ^ { 3 } + 5 x - 9 } { x ^ { 2 } + 4 x - 21 }$