Answer
Then $f$ is discontinuous at $x=1$; it is right-continuous there.
$f$ is discontinuous at $x=3 ;$ it is neither left-continuous nor right-continuous there.
$f$ is discontinuous at $x=5$; it is left-continuous there.
None of these points of discontinuity are removable.
Work Step by Step
From the given figure, we have
$$\lim_{x\to 1^-}f(x)=f(1)=2$$
and\begin{align*}
\lim_{x\to 3^-}f(x)&=2.5 \\
\lim_{x\to 3^+}f(x)&=4.5\\
f(3)&=1
\end{align*}
and \begin{align*}
\lim_{x\to 5^-}f(x)&=1.5 \\
\lim_{x\to 5^+}f(x)&=3.5\\
f(5)&=1 .5
\end{align*}
Then $f$ is discontinuous at $x=1$; it is right-continuous there.
$f$ is discontinuous at $x=3 ;$ it is neither left-continuous nor right-continuous there.
$f$ is discontinuous at $x=5$; it is left-continuous there.
None of these points of discontinuity are removable.
