Given the sinusoidal function:
[tex]f(x)=A\sin (x)[/tex]
Where A is the amplitude. Looking at the graph, the function is translated 4 units up and shifted π/3 units to the right. Additionally, we note that the amplitude is 10.
Finally, we see that the period is π. Using this information, the function is:
[tex]f(x)=10\sin (2x-\frac{2\pi}{3})+4[/tex]
This function can be obtained from the initial 10sin(x) function making the following transformations:
- Shift 4 units up: f(x) + 4
- Shift π/3 units to the right: f(x - π/3) + 4
- Shrink by a factor of 2: f(2*(x - π/3)) + 4 = f(2x - 2π/3) + 4
