Question

PLZ HELP!!

Graph a sine function whose amplitude is 3, period is 4pi, midline is y=2, and y-intercept is (0,2). The graph is not a reflection of the parent function over the x-axis.
Use the sine tool to 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.

Answer 1

Plot Points: (0,2) (3.14,5)

Answer 2

The sin function is
`y=3 sin((1)/(2)x)+2`

Maximum point is
`(\pi,5)`

Explanation:

Given : A sine function whose amplitude is 3, period is
`4\pi`, midline is y=2, and y-intercept is (0,2). The graph is not a reflection of the 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=3 , C=2

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

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

The sin function is
`y=3 sin((1)/(2)x)+2`

Now, We plot the graph of the sin function.

The graph is attached below.

First point is midline i.e, (0,2)

Maximum point is
`(\pi,5)`