Answer
Please see below.
Work Step by Step
As we see the graph of $f(x)=[x]-x$, we find that the function is discontinuous at integer points $\mathbb{Z}$ because the left- and right-handed limits at these points are different:$$\lim_{x \to n^-}f(x)=-1, \qquad \lim_{x \to n^+}f(x)=0 \qquad n \in \mathbb{Z}$$
