Answer:
y = -3sin(2(x+π/8)) +2
Explanation:
The point at (-π/8, 2) is in the middle of the graph of the function so suggests a suitable starting point for a transformation of a sine function.
That point has a vertical offset of 2 and a horizontal offset of -π/8.
The graph goes up 3 units from that point, so the vertical scale factor is 3.
The horizontal distance from centerline to extreme is π/4, which is half that of a sine function, so the horizontal scale factor is 1/2.
The intial direction is negative from the point (-π/8, 2), so the vertical scale factor is negative (-3, not +3).
Putting these into the form
... g(x) = (vertical scale factor) × f((x - (horizontal offset))/(horizontal expansion factor)) - (vertical offset)
we have ...
... y = -3 × sin((x + π/8)/(1/2)) +2
We can simplify a bit to ...
... y = -3·sin(2(x +π/8)) +2
