Question

A sine function has the following key features:

Frequency=1/8pi


Amplitude= 6


Midline: y=3

Y-intercept: (0,3)


The function is not a reflection of its parent function over the x-axis.


Use the sine took to graph the function. The first point must be on the midline and the second point must be the maximum or minimum value on the graph closest to the firsr point.

Answer 1

The sin function is
`y=6sin((1)/(4)x)+3`

Explanation:

Given : A sine function has the following key features:

Frequency =
`(1)/(8\pi)`, Amplitude = 6, Midline: y = 3, y-intercept: (0,3)

The function is not a reflection of its parent function over the x-axis.

To plot the graph :

Solution :

General form of sin function is
`y=A sin(Bx)+C`

Where A is the amplitude

`B=\frac{2\pi}{\text{Period}}`

C is the midline

Substitute the given key features,

A=6 , C=3

Period= 1/Frequency

`P=8\pi`

`B=(2\pi)/(8\pi)=(1)/(4)`

The sin function is
`y=6sin((1)/(4)x)+3`

The function is not a reflection of its parent function over the x-axis.

The sin function is
`y=6 sin((1)/(4)x)+3`

The graph is attached below.