## Calculus (3rd Edition)

$f(x)=[\frac{1}{2}x]$, 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 $$\lim _{x \rightarrow 2n+}[x]=n, \quad f(2n)=n.$$