The sine function is:
f(x) = -2*sin(x/2) + 3.
So you got it almost correctly, you only forgot to apply the reflection.
How to get the sine function?
We start with the general sine function:
[tex]a*g(w*x + p) +m[/tex]
where g(x) = sin(x)
- a is the amplitude, which we know is equal to 2.
- w depends on the period.
- M is the midline, which we know is equal to 3.
- p is the phase shift, because the y-intercept is (0, 3) we know that:
f(0) = 2*sin(w*0 + p) + 3 = 3
= 2*sin(p) + 3 = 3
Then we must have p = 0, so there is no phase shift.
We also know that we have a reflection over the x-axis of the parent sine function, we would actually have:
f(x) = 2*-sin(wx) + 3
Finally, to get the value of k we know that the period of the general sine function is 2*pi, while here is 4*pi, then we must have w = 1/2 to get the correspondent correction, so the function is:
f(x) = -2*sin(x/2) + 3.
This is almost the same thing that you got in the graph, where you only forgot to apply the reflection over the x-axis of the parent function.
If you want to learn more about sinusoidal functions, you can read:
https://brainly.com/question/18055768
