# How do you find the period of y = 1 + tan(1/2x)?

$2 \pi$
The period of $\tan \left(x\right)$ is $\pi$. The period of a function of the form $f \left(x\right) = A + B \tan \left(C x\right)$ is $\frac{\pi}{|} C |$ (the $A$ and $B$ are irrelevant in determining the period).
For your problem, $C = \frac{1}{2}$ so $| C | = \frac{1}{2}$ and $\frac{\pi}{|} C | = \frac{\pi}{\frac{1}{2}} = 2 \pi$.