Respuesta :
Answer:
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;
[tex]y = A\sin(B(x+C))+D[/tex] where
if A >1, Vertical stretch and
if 0<A<1, Vertical compression
Period is [tex]\frac{2\pi}{B}[/tex]
Phase shift is C (Positive is to left)
Vertical shift is D.
Given the function:
[tex]y = \frac{1}{4}\sin(4(x+\frac{\pi}{6}))[/tex]
here,
[tex]A = \frac{1}{4} < 1[/tex], B = 4 , [tex]C= \frac{\pi}{6}[/tex] and D = 0
Therefore, transformation are needed on sine function to get [tex]y = \frac{1}{4}\sin(4(x+\frac{\pi}{6}))[/tex]
Vertical compression of [tex]\frac{1}{4}[/tex]
Horizontal stretch to a period = [tex]\frac{2 \pi}{4} = \frac{\pi}{2}[/tex]
Phase shift = [tex]\frac{\pi}{6}[/tex] units to left.
