Answer
$y = -2+3~tan~(4x+\pi)$
We can see the graph below.
Work Step by Step
$y = -2+3~tan~(4x+\pi)$
When $x = \frac{\pi}{8}$, then $y = -2+3~tan~\frac{3\pi}{2}~~$ (which is undefined)
When $x = \frac{3\pi}{16}$, then $y = -2+3~tan~\frac{7\pi}{4} = -5$
When $x = \frac{\pi}{4}$, then $y = -2+3~tan~2\pi = -2$
When $x = \frac{5\pi}{16}$, then $y = -2+3~tan~\frac{9\pi}{4} = 1$
When $x = \frac{3\pi}{8}$, then $y = -2+3~tan~\frac{5\pi}{2}~~$ (which is undefined)
We can see the graph below.