Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 67: 21

$ f(x)=[\frac{1}{2}x]$, has a jump discontinuity at $ x=2n $ for every integer $ n $,

The function $ f(x)=[\frac{1}{2}x]$, has a jump discontinuity at $ x=2n $ for every integer $ n $, since $$\lim _{x \rightarrow 2n+}[x]=n, \quad \lim _{x \rightarrow 2n-}[x]=n-1.$$ Moreover, $ f(x)=[x]$ is right-continuous because $$\lim _{x \rightarrow 2n+}[x]=n, \quad f(2n)=n.$$