Sketch the graphs of the following functions :

f(x) = 2 sin πx, 0 ≤ x ≤ 2.

We know that g (x) = sin x is a periodic function with period 2π.

∴ f (x) = 2 sin πx is a periodic function with period 2. So, we will draw the graph of f (x) = 2 sin πx in the interval [0, 2]. The values of f (x) = 2 sin πx at various points in [0, 2] are listed in the following table:

By plotting the above points, we obtain the required curve.