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.

Guest Feb 9, 2018

#1**+2 **

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

CPhill Feb 9, 2018