Describe all of the transformations from the basic graph for

Describe all of the transformations from the basic graph for each of the given functions:

Be sure to give any changes in amplitude (or vertical stretch), period, and direction and amount of each shift.

a) y = -1/3 cos(x+pi/6)+2                                                 b) y = 2tan(4x-pi/6)

Solution

a) y = -1/3 cos(x+pi/6)+2

basic function : y = cosx

vertical shrink by 3 units : y = 1/3cosx

Reflect across x axis: y = -1/3 cosx

No change in period

phase shift = pi/6 to left

Vertical shift by 2 units up

b) y = 2tan(4x - pi/6)

Basic function y = tanx

horizontal shrink by 4 units in period y = tan(4x)

vertical stretech by 2 units: y =2tan(4x)

No vertical shift

phase shift to right by pi/6