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# A sine function has the following key features:

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A sine function has the following key features:

Period = 4π

Amplitude = 2

Midline: y = 3

y-intercept: (0, 3)

The function is 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.

Feb 9, 2018

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A sine function has the following key features:

Period = 4π

Amplitude = 2

Midline: y = 3

y-intercept: (0, 3)

The function is 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.

In the form

y    =  Asin (Bx) + c

A=  the amplitude  =  2

B  =  2pi  / period  =  2pi / [ 4pi]  =  (1/2)

C =  the value of the midline  =  3

If this function is a reflection of its parent function over the x axis, the parent function must be :

y  =  -2sin ( (1/2) x)   - 3

So....our function is

y = 2sin ( (1/2) x )  + 3

See the parent  and the reflected function, here :  https://www.desmos.com/calculator/5o7wtmtgsb   Feb 9, 2018