Determine the equation from the graph. i dont know how do this problem : ( the graphing is not my best friend : s

y = -3sin(2(x+π/8)) +2

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