Compare this graph to a sine plot !!
y values range from -2 to 4 (a range of 6; an amplitude of 3). A typical sine plot ranges from -1 to +1 (an amplitude of 1), so this is 3 times as much and y is +1 more. That makes A=3 and D=1.
y = 3 sin(Bx-C) + 1 [so far]
Note that the period of a sine plot is from 0 to 2π and the sin(x)=0 at x=0, x=π and x=2π . Here, the x-values are 1/2 of those (see red line in my figure), so they must be multiplied by B=2 They are not offset, so C=0)
The result is:
y = 3 sin(2x) + 1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
- vertical shift is D