Question

The vertical asymptote(s) of the graph $y=\frac{x}{x^2-4}$ is/are:

• A. $x=2$ only
• B. $y=2$ only
• C. $x=2$ and $x=-2$
• D. $y=2$ and $y=-2$
• E. $x=2,x=-2$ and $x=0$

Answer 1

Answer: (C)

$x=2$ and $x=-2$

For vertical asymptote, the condition is $y$ should be infinite, which implies $x^2-4=0$.
$x^2-4=(x-2)(x+2)=0$, which implies $x=-2,2$.