Wrong pgfplots plot for function with vertical asymptote

Question

I want to plot the function $\frac{3 x}{1 + x}$ with pgfplots. Using

\begin{tikzpicture}
    \begin{axis}[axis x line=none, axis y line=none, no markers]
        \addplot {3 * x / (1 + x)};
    \end{axis}
\end{tikzpicture}

I get this:

This is obviously wrong. The same function plotted in Grapher.app:

Answer 1

You can set restrict y to domain=-20:20. That will discard all coordinates that are outside that range, and the plot will be interrupted. You should make sure that the specified range is somewhat larger than the visible axis limits, otherwise the plot might not extend all the way to the edges.

\documentclass[a4paper,12pt, border=5mm]{standalone}
\usepackage{pgfplots}

\begin{document}%
\begin{tikzpicture}
    \begin{axis}[
        axis lines*=middle,
        no markers,
        ymin=-5, ymax=10,
        enlarge y limits=true,
        enlarge x limits=false,
        restrict y to domain=-20:20]
        \addplot [thick, samples=50, smooth] {3 * x / (1 + x)};
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

One possible (not very elegant) solution is to split the plot at the asymptote:

\begin{tikzpicture}
    \begin{axis}[
        height=10cm,
        width=10cm,
        xmin = -5,
        xmax = 5,
        ymin=-10,
        ymax=10,
        grid=major,
        samples=100,
        enlargelimits=false,
        legend pos= north east
    ]

    \addplot+[mark=none, smooth,domain=-10:-1.05,draw=blue] {(3 * \x) / (1 +
      \x)};
    \addplot+[mark=none, smooth,domain=-0.95:10,draw=blue] {(3 * \x) / (1 + \x)};


    \end{axis}
\end{tikzpicture}

Ideally, I would like something that works automatically, without needing to know the asymptote.