Find all vertical asymptotes for the given function. $y = \frac { 5 x } { 4 - x ^ { 2 } }$
A) $x = 0$
B) $x = \pm 2$
C) $x = 2$
D) $x = - 2$
E)no vertical asymptotes

Question

Quizplus · Accepted Answer

Vertical asymptotes occur where the denominator of a rational function is zero (as long as the numerator is not zero at the same point, which would indicate a hole instead). For the given function $y = \frac { 5 x } { 4 - x ^ { 2 } }$, setting the denominator equal to zero gives $4 - x^2 = 0$, which solves to $x^2 = 4$. Taking the square root of both sides gives $x = \pm 2$, indicating vertical asymptotes at $x = 2$ and $x = -2$.

Find All Vertical Asymptotes for the Given Function y=5x4−x2y = \frac { 5 x } { 4 - x ^ { 2 } }y=4−x25x​

Find All Vertical Asymptotes for the Given Function $y = \frac { 5 x } { 4 - x ^ { 2 } }$