g is a trigonometric function of the form g(x) = a sin(bx + c) + d. Below is the graph g(x). The function intersects its midline at 3/4 *pi, 3) and has a maximum point at (pi,7) Find a formula for g(x). Give an exact expression.

Step-by-step explanation:

Because the function intersects its midline at , then the midline is .

Additionally, the amplitude is just the positive distance between the maximum/minimum and the midline, so the amplitude is .

Also, given that period is and the fact that the period is from our given maximum, we have the equation where .

Lastly, to find , we know that the phase shift, , is (or to the left) since . Therefore, we have the equation where .

Putting it all together, our final equation is

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