a) y=csc(x-3)

I understand that there are asymptotes at 0, pi, and 2pi and I know how to graph the base points but I am confused on how to move it with the phase shift.

Do I use a table of value for the asymptotes and base points to move?

asymptotes at 0, pi, and 2pi

means at
x-3 = 0 or x = 3

x-3 = pi or x = pi + 3

x-3 = 2 pi or x = 2 pi + 3