So,
As we can see, the graph of the function given is a periodic function because it repeats constantly.
This graph has asymptotes (it is not defined) each pi/2 units, so, this graph clearly represents a function based in tan(x).
Now, notice that this graph is a represents a reflection of y=tanx. So, the first change we're going to do is to put a negative sign backwards the function tan(x). This is, y=-tan(x)
Now, notice that this fuction has a period equal to pi/2, and it is out of phase by pi/2 units.
So, this function has the equation:
[tex]y=-\tan (\frac{\pi}{2}x-\frac{\pi}{2})[/tex]
