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

1 Answer | Add Yours

lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

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 formĀ  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 atĀ `((3pi)/8+pi/2k,-3)` .

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

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 2)
This image has been Flagged as inappropriate Click to unflag
Image (2 of 2)

We’ve answered 318,918 questions. We can answer yours, too.

Ask a question