Question

What does it mean when you need to graph a piecewise function where f(x) =0 if x is not an integer

Answer 1

It means that the graph is discontinuous. It consists of a line that looks like the x axis, but at every integer value of x there will be a hole. The piecewise function will probably contain f(x)=1 or some other function for x equal to an integer. This other function will also be discontinuous because it will consist of isolated points separated by gaps.