Graph y=3sin(4x) Include min, max, and intercepts. Label with points on the unit circle.

Expert Answers
lemjay eNotes educator| Certified Educator

To graph the function

`y=3sin(4x)`

we may apply transformation of function. Since it is a sine function, the parent function is y=sinx. (See first image for the graph of y=sinx.)

Then, express the given function in the form  y =Asin(Bx -C)+D.

So it becomes:

`y=3sin(4x - 0) + 0`

Then, apply the formula:

Amplitude=A

Period=`(2pi)/B`

Phase Shift=`C/B`

Vertical Shift=D

Since the values of A=3, B=4, C=0 and D=0, then, the given function would have the following properties:

Amplitude=3

Period=`pi/2`

Phase Shift=0

Vertical Shift =0

Then, use these to transform the graph of y=sinx.

See second image for the graph of y=3sin(4x).

Notice that in the graph, the maximum points occur at `(pi/8+pi/2k,3)` .

The minimum points occur at `((3pi)/8+pi/2k,-3)` .

And the x-intercepts occur at `(0,0)` , `(pi/4+pi/2k,0)` and `(pi/2+pi/2k,0)` .

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