What are the period and phase shift for f(x) = −4 tan(x − π)?

with that template in mind, let's see this one.

The general form for the tangent equation is y = (a)tan(bx-c)+d where a is the amplitude, b is the period and c is the phase shift.  The period of the tangent graph is pi, and the formula to solve for the period is then .  Our b value is 1, so the period of this tangent curve is pi.  The formula for the phase shift is and for us that is pi/1.  So the period for this curve is pi, and the phase shift is pi units to the right.

Main idea on left, details on right