The correct option will be the last one: [tex] f(x)= 9sin(6 \pi x)+6 [/tex]
Explanation
The general equation for sinusoidal function is: [tex] f(x)= Asin(2\pi fx)+b [/tex], where [tex] A= [/tex]Amplitude, [tex] f= [/tex] frequency and [tex] b= [/tex] 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, [tex] A= \frac{18}{2}=9 [/tex]
Frequency [tex] (f) [/tex] is given as 3 and y-intercept[tex] (b) [/tex] is 6
So, the required function will be:
[tex] f(x)= 9sin(2\pi*3x) +6\\ \\ f(x)= 9sin(6\pi x) +6 [/tex]
