Which transformations are needed to change the parent sine function to
y=1/4sin(4(x+pi/
a.) vertical stretch of 1/4, horizontal stretch to a period of 2pi, phase shift of pi/6 units to the left
b.)vertical compression of 1/4, horizontal compression to a period of pi/2, phase shift of pi/6 units to the left
c.)vertical stretch of 4, horizontal stretch to a period of 8pi, phase shift of pi/6 units to the right
d.)vertical compression of 4, horizontal compression to a period of pi/4, phase shift of pi/6 units to the right

Option B is correct.

Transformation needed are;

Vertical compression of 1/4,

horizontal compression to a period of pi/2,

phase shift of pi/6 units to the left.

Step-by-step explanation:

The formula for the general Sine function is given by;

where

if A >1, Vertical stretch and

if 0<A<1, Vertical compression

Period is

Phase shift is C (Positive is to left)

Vertical shift is D.

Given the function:

here,

, B = 4 , and D = 0

Therefore, transformation are needed on sine function to get

Vertical  compression of

Horizontal stretch to a period =

Phase shift = units to left.

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