Question

Identify the phase shift of each function. Describe each phase shift ( use a phrase like 3 units to the left):

Answer 1

ANSWER

Phase shift: 0.5 units to the left

EXPLANATION

The given function is


`y = 2 - 3 \cos(2x + 1)`

The phase shift is the same as the horizontal translations.

Comparing to


`y=A\cos(Bx+C)+D`

The vertical shift is D=2 units up.

The horizontal shift is


`(C)/(B) = (1)/(2)`

units to the left.

Answer 2

The phase shift will be 0.5 (0.5 to the right)

Explanation:

The Phase Shift is how far the function is shifted horizontally from the usual position.

Therefore;

y = A sin(B(x + C)) + D

The phase shift is C (positive to the left)

The function;

y = 2 - 3 cos (2x + 1)

We could write the function in the form of y = A sin(B(x + C)) + D

we have; y = 2 - 3 cos (2x + 1),

we get y = 2 - 3 Cos (2(x - 0.5)

Therefore; the phase shift will be -0.5 (0.5 to the right)