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?

We can start by examining the general form of a sinusoidal function.
[tex]y=asin(bx+c)+k[/tex]
Now let's examine all these parameters and see what they do. This will allow us to construct the required function. 
Parameter a will scale the function. It will make the sine wave bigger or smaller. If a>1 it will make the wave bigger, if a<1 it will make the wave smaller. If a<0 it can flip the function around x-axis and scale it at the same time.
Parameter b will shrink the functions. I will either increase it's frequency or decrease it. The frequency of a sine wave is [tex]w= \frac{2 \pi }{b} [/tex].
Parameter c will slide the function left or right. This parameter is called the phase. If c>0 graph is shifted to the left, if c<0 graph is shifted to the right.
Lastly, we examine parameter k. This parameter will simply slide the function up or down. If k>0 graph is shifted up, if k<0 graph is shifted down.
So now let us go over each requirement.
Frequency must be 3. From this, we find parameter b.
[tex]3= \frac{2 \pi }{b} [/tex]
[tex]b= \frac{2}{3} \pi [/tex]
In order to get the maximum value of 15 and minimum of -3, we need to tweak parameters a and k. Parameter a is maximum value plus absolute minimum value divided in half. So a is 9. Now we need to shift our function up by tweaking parameter k. In order to get the maximum value of 15, we need to set k=6.
Lastly, we need to find our phase or parameter c. If we evaluate our function at x=0 we find that y(0) is actually 6. This happens because of parameter k. 
So we don't have to tweak parameter c, we can set it to be 0.
Our final function is:

[tex]y(x)=9sin( \frac{2 \pi x}{3})+6[/tex]