Question

A sine function has the following key features:

Frequency = 1/6π
Amplitude = 2
Midline: y = 3
y-intercept: (0, 3)
The function is not a reflection of its parent function over the x-axis. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

Answer 1

we got this form..

Explanation:

y = A sin (Bx + C ) + D

A = the amplitude = 2

B.....shows the number of periods in 2pi

The frequency = 1/6pi = 1 / period......so the period is 6pi

To find "B" we have 2pi / [ 6 pi ] = (1/3)

C = the phase shift..there is none....so "C" = 0

D = the shift up/down.....the normal y intercept for the sine is (0, 0)....so....the shift up = 3 units....sice the y intercept = (0, 3)

So....the function is

y = 2sin (x/3) + 3