Question

Which transformations are needed to change the parent sine function to

y=1/4sin(4(x+pi/6))?

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

Answer 1

B

Explanation:

Answer 2

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.

Explanation:

The formula for the general Sine function is given by;

`y = A\sin(B(x+C))+D` where

if A >1, Vertical stretch and

if 0<A<1, Vertical compression

Period is
`(2\pi)/(B)`

Phase shift is C (Positive is to left)

Vertical shift is D.

Given the function:

`y = (1)/(4)\sin(4(x+(\pi)/(6)))`

here,

`A = (1)/(4) < 1`, B = 4 ,
`C= (\pi)/(6)` and D = 0

Therefore, transformation are needed on sine function to get
`y = (1)/(4)\sin(4(x+(\pi)/(6)))`

Vertical compression of
`(1)/(4)`

Horizontal stretch to a period =
`(2 \pi)/(4) = (\pi)/(2)`

Phase shift =
`(\pi)/(6)` units to left.