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

A. Vertical stretch of 1/4 hortionzal stretch to a period of 2pi , phase shift of pi/6 units to the left

Answer 2

B

Explanation:

The parent sine function is given by y=sin(x). For this function we have the following data

Period:2
`\pi`

Phase Shift: 0 for Phase Shift is given by y=sen(x-k)=senx Then sin(x-0)=sinx

-k=0

When we transform this function, dilating it, we multiply the function by 1/4 or divide by 4, so we compress it. And Increase the phase shift by adding values to the x, like it was done in

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

Period:
`(\pi)/(2)`

Phase shift: - (
`\pi`/6) For y=1/4 sin[4(x+pi/6)] as the sign of
`+(\pi)/(6)` the phase shift is actually
`-(\pi)/(6)` units, or
`(\pi)/(6)` to the left.