A sinusoidal function whose frequency is 3, maximum value is 15, minimum value is -3 has a y-intercept of 6. Which function could be the function described?

a. f(x)=9sin(x/3)+6
b. f(x)=9sin(6pix)+3
c. f(x)=9sin(3x)+3
d. f(x)=9sin(6pix)+6

please explain if you can, if not that’s ok!

A. f(x) = 9sin(x/3) + 6

Step-by-step explanation:

First, we can eliminate B and C because they have the wrong vertical shift.

Since the y intercept is 6, this means the function has a vertical shift up 6 units, represented by a +6 at the end of the equation.

The amplitude is 9, found by calculating the difference between the minimum and maximum values, and dividing it by 2.

(15 - (-3)) / 2

18 / 2

= 9

Using a calculator, find the period given the frequency.

The period (coefficient of x) is 1/3.

So, putting all of these constants together, the correct equation is:

A. f(x) = 9sin(x/3) + 6

A. f(x) = 9sin(x/3) + 6

Step-by-step explanation:

Hope this will help

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