Question: The function f is defined, for 0 <= x <= pi radians, as f(x) = 3 sin (x/2) - 2. Sketch the graph of y = f(x).

Approach:
The usual sine curve has an amplitude of 1 unit and a period of 2 pi radians, so we have

0 <= x/2 <= 2 pi, which leads to 0 <= x <= 4 pi.

Note that we are stretching the curve horizontally so that it is twice as long as before.

When we sketch y = f(x) for the interval [0, pi], it'll be a quarter of the original sine curve.

Next, we stretch the sine curve vertically so that its amplitude is 3 units (i.e. thrice as tall as before).

Finally, we shift the entire curve down by 2 units.

The result looks like this: