Question

Answer question number 18. The question is in the image.

Answer 1

18.

Given:

`g(x)=3sin2x`

Required:

We need to graph the function and find the transformation from the parent function.

Step-by-step explanation:

The given equation is of the form.

`g(x)=Asin(Bx+C)`

where A =3, B=2, and C=0.

We know that A is amplitude.

`Amplitude=3`
`Period=(2\pi)/(|B|)`

Substitute B=2 in the equation,

`Period=(2\pi)/(|2|)`
`Period=\pi`

Recall that the amplitude of a function is the amount by which the graph of the function travels above and below its midline.

The distance between the maximum point and midline is 3.

The time interval between two waves is known as a Period

The time interval between two waves is pi.

The graph of the function.

`The\text{ parent function is f\lparen x\rparen=sinx.}`

Recall that the amplitude stretches or compresses the graph vertically.

Here we have amplitude =3. it is a positive value.

The parent function stretches vertically by 3 units.

Recall that the period stretches or compresses the graph horizontally.

Here we have the period is pi.

The parent function compresses horizontally by pi.

Final answer:

`Amplitude=3`

`Period=\pi`

The transformation is stretched vertically by 3 units and compressed horizontally by pi.