I have done this problem a few times, keep getting different graph from what the book has. Could some one solve this please. Y= -1+1/2cot(2x-3pi)

My fist step was to factor out the 2 so, Y=-1+1/2cot2(x-3pi/2).

Then I found the Period which was Pi/2.

Then I set (x-3pi/2)=0 and (x-3pi/2)=pi/2, which tells what the asymptotes....Not sure what I'm doing wrong.