Question

Graph the function $f\left(x\right)=\frac{x-4}{x^2-4}$ and find asymptotes of $f\left(x\right)$ if any.

• A. $x=4$
• B. $x=\pm 4$
• C. $x=\pm 2$
• D. $x=2$

Answer 1

The correct option is C $x=\pm 2$

$f\left(x\right)=\frac{x-4}{x^2-4}$

Asymptotes is the line along which the curve ggrazes.

$\Rightarrow f\left(x\right)\to \infty \Rightarrow x^2-4=0\Rightarrow x^2=4\Rightarrow x=\pm 2$

So option $C$ is correct.