tikz problem (non-continuous function)

Question

I want to plot a function x^3/(x^2-1) but it doesn't work.

\documentclass{article}    
\usepackage{tikz}

\begin{document}

  \begin{tikzpicture}[domain=-5:5,smooth]
    \draw[->] (-5,0) -- (5,0) node[right] {$x$}; 
    \draw[->] (0,-5) -- (0,5) node[above] {$y$};
    \draw [color=blue, thick] plot ({\x},{pow(\x,3)/(pow(\x,2)-1)});
  \end{tikzpicture}

\end{document}

It does something like this. It should be non-continuous function, not this.

How to fix it? Thanks.

Answer 1

If using pgfplots would be ok for you then you could avoid such problems. Instead of the standalone class you can, of course, use any other documentclass you like.

Edit: I pimped my example a little. If you want to label some points or add function definitions etc. to your plot you can do this like in any other tikzpicture: creating nodes and drawing works in the same way as usual. To make your life easy you can access the in-plot coordinates via axis cs:, so if you want to create a node at the in-plot point x=1 and y=0 you can use something like \node at (axis cs:1,0) {$x=1$};.

\documentclass{standalone}

\usepackage{pgfplots}

\begin{document}
  \begin{tikzpicture}
    \begin{axis}[
        restrict y to domain=-5:5,
        samples=1000,
        ticks=none,
        xmin = -5, xmax = 5,
        ymin = -5, ymax = 5,
        unbounded coords=jump,
        axis x line=middle,
        axis y line=middle,
        xlabel={$x$},
        ylabel={$y$},
        x label style={
          at={(axis cs:5.02,0)},
          anchor=west,
        },
        every axis y label/.style={
          at={(axis cs:0,5.02)},
          anchor=south
        },
        legend style={
          at={(axis cs:-5.2,5)},
          anchor=west, font=\scriptsize
        }
        ]

      \addplot[color=blue, mark=none, domain=-5:5] {x^3)/((x^2) - 1)};
      \addlegendentry[blue]{$f(x)=\frac{x^3}{x^2 - 1}$}
      \draw[dashed] ({axis cs:1,0}|-{rel axis cs:0,1}) -- ({axis cs:1,0}|-{rel axis cs:0,0});
      \draw[dashed] ({axis cs:-1,0}|-{rel axis cs:0,1}) -- ({axis cs:-1,0}|-{rel axis cs:0,0});
      \node[below right, font=\scriptsize] at (axis cs:1,0) {$x=1$};
      \node[below left, font=\scriptsize] at (axis cs:-1,0) {$x=-1$};
    \end{axis}
  \end{tikzpicture}
\end{document}

Edit:

Here is a pure tikz solution. It's not very elegant but in case one doesn't want to use pgfplots it might be a good starting point.

 \documentclass{standalone}    
 \usepackage{tikz}

 \begin{document}

   \begin{tikzpicture}[smooth, scale=0.5]
        \pgfmathsetmacro\ymax{pow(1.05,3)/(pow(1.05,2)-1)}
        \draw[->] (-10,0) -- (10,0) node[right] {$x$}; 
        \draw[->] (0,-\ymax) -- (0,\ymax) node[above] {$y$};
        \draw [color=blue, thick, domain=-10:-1.05, samples=200] plot ({\x},{pow(\x,3)/(pow(\x,2)-1)});
        \draw [color=blue, thick, domain=-0.96:0.96, samples=200] plot ({\x},{pow(\x,3)/(pow(\x,2)-1)});
        \draw [color=blue, thick, domain=1.05:10, samples=200] plot ({\x},{pow(\x,3)/(pow(\x,2)-1)});
        \draw [color=black, dashed] (-1, -\ymax) -- (-1, \ymax);
        \draw [color=black, dashed] (1, -\ymax) -- (1, \ymax);

   \end{tikzpicture}

\end{document}