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.

graph the function. 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.

kikidylm Jan 23, 2019

#1**+1 **

We have this form

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

Here is the graph : https://www.desmos.com/calculator/tlcanknjtl

CPhill Jan 23, 2019