Question

Can you check my question please? thanks for your help.

Answer 1

The correct option will be the last one:
`f(x)= 9sin(6 \pi x)+6`

Step-by-step explanation

The general equation for sinusoidal function is:
`f(x)= Asin(2\pi fx)+b`, where
`A=`Amplitude,
`f=` frequency and
`b=` y-intercept

Here the maximum value is 15 and the minimum value is -3. So, the distance between maximum and minimum values is 18. That means, the Amplitude,
`A= (18)/(2)=9`

Frequency
`(f)` is given as 3 and y-intercept
`(b)` is 6

So, the required function will be:

`f(x)= 9sin(2\pi*3x) +6\\ \\ f(x)= 9sin(6\pi x) +6`