# What are the asymptotes of f(x) = tan(2x)?

${45}^{\circ} , {135}^{\circ} , {225}^{\circ}$ etc.
$f \left(x\right) = \tan \left(2 x\right)$ is the function $f \left(x\right) = \tan \left(x\right)$ stretched by a factor of $\frac{1}{2}$ parallel to the x axis.
Since the asymptotes of $\tan \left(x\right)$ are ${90}^{\circ} , {270}^{\circ} , {450}^{\circ}$ etc. , the asymptotes of $\tan \left(2 x\right)$ will be half of these: