\textbf{16.} For a specific value of $k$, the function
$$f(x) = \begin{cases} |x - [-x]| & x \in [x] \text{ even} \\ x - [x] + k & x \in [x] \text{ odd} \end{cases}$$
is continuous at $x = n$ and $x = -n$. Which case is correct regarding $n$ specifically? $(k, n \in \mathbb{N})$
\begin{itemize}
\item[(1)] $n$ even
\item[(2)] $n$ odd
\item[(3)] $f$ is continuous for all values of $n$.
\item[(4)] $f$ is not continuous for any value of $n$.
\end{itemize}
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