How to Graph Floor/Ceiling Functions in LaTeX (PGFPlots)

You can use the jump mark mid style for this, which draws horizontal unconnected line segments.

\begin{tikzpicture}
\begin{axis}[axis lines=middle]
\addplot [
    jump mark mid,
    domain=-3:3,
    samples=100,
    very thick, red
] {floor(3*x)+2};
\end{axis}
\end{tikzpicture}

to get

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A fancier approach could be to use the discontinuous style from the question Probability density function of Uniform Distribution to plot the intervals.