What are the period and phase shift for f (x) = 3 tan (4x + π) ?

For an equation y = a tan[b (x+c) ], the period is equal to 2*pi/b, while the phase shift is c.

This equation can be rewritten as:

f (x) = 3 tan [4 (x + pi/4) ]

In this case, b = 4, c = pi/4

Then the period = 2*pi/b = pi/2.

The phase shift = pi/4 (to the left).