# What are the important information needed to graph y = tan (x + pi/3) ?

You are changing a function by adding something to its argument, i.e., you're passing from $f \left(x\right)$ to $f \left(x + k\right)$.
This kind of changes affects the graph of the original function in terms of a horizontal shift: if $k$ is positive, the shift is toward the left, and vice versa if $k$ is negative, the shift is to the right.
So, since in our case the original function is $f \left(x\right) = \tan \left(x\right)$, and $k = \frac{\pi}{3}$, we have that the graph of $f \left(x + k\right) = \tan \left(x + \frac{\pi}{3}\right)$ is the graph of $\tan \left(x\right)$, shifted $\frac{\pi}{3}$ units to the left.