You're gping to have major problems because the input (x, f(x)) is discontinuous (not exactly, but sort of).
Therefore, your NN will have to literally memorize the x-f(x) mapping given the large discontinuities.
One approach is to use a four-layer NN which can address the discontinuities.
But really, you may simply want to look at other smoothening methods rather than NN for thos problem.
You have a periodic function so first of all, only use one period, or you will memorize and not generalize.