Question

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

Answer 1

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

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, $A= \frac{18}{2}=9$

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

So, the required function will be:

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