# What are the horizontal and vertical asymptotes of: f(x)=xtan(x)?

Apr 23, 2018

$x \ne \frac{\pi}{2} + k \pi , k \in \mathbb{Z}$

#### Explanation:

$\tan \left(x\right)$ is undefined for $\frac{\pi}{2} + k \pi$ where $k \in \mathbb{Z}$

For example: $\frac{\pi}{2} , \frac{3 \pi}{2} , \frac{5 \pi}{2.} . .$

Therefore there will be vertical asymptotes at every $\frac{\pi}{2} + k \pi$

There are no horizontal asymptotes, however, as the range is $y \in \mathbb{R}$

graph{xtan(x) [-5.55, 5.55, -2.775, 2.774]}