Plot in TikZ: f(x) = 1/(x – 2) + 3

Question

I am trying to plot the function f(x) = 1/(x-2) + 3 using TikZ, however I get that the domain is undefined.

What code should I type?

Answer 1

You can use pgfplots instead:

\documentclass{article}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[axis lines=middle,samples=200]
\addplot[blue,domain=-3:1.85] {1/(x-2) +3 };
\addplot[blue,domain=2.15:6] {1/(x-2) + 3};
\draw[red!20,dashed] (axis cs:2,-4) -- (axis cs:2,10);
\end{axis}
\end{tikzpicture}

\end{document}

Adding some more labels:

\documentclass{article}
\usepackage{pgfplots}

\pgfplotsset{every tick label/.style={inner sep=0pt,font=\scriptsize}}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  axis lines=middle,
  samples=200,
  xtick={-3,...,6},
  ytick={-3,...,9}
]
\addplot[blue,domain=-3:1.85] {1/(x-2) +3 };
\addplot[blue,domain=2.15:6] {1/(x-2) + 3};
\draw[red!20,dashed] (axis cs:2,-4) -- (axis cs:2,10);
\end{axis}
\end{tikzpicture}

\end{document}

Answer 2

Whatever your problem was, split the function at x = 2.

In my answer I provide two ways: pgfplots and vanilla TikZ.

MWE

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    ymin=-5,
    ymax=5,
    xmin=-10.1,
    xmax=10.1,
    axis on top=true,
    axis x line=middle,
    axis y line=middle,
    ]
    \addplot [forget plot, samples=100, domain=-10:1.99] {1/(x-2) + 3};
    \addplot [             samples=100, domain=2.01:10] {1/(x-2) + 3};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}[scale=.3]
    \draw plot [
        samples=100,
        domain=-10:1.9
        ] (\x,{1/(\x-2) + 3});
    \draw plot [
        samples=100,
        domain=2.1:10
        ] (\x,{1/(\x-2) + 3});
\end{tikzpicture}
\end{document}

Output (pgfplots)

Output (vanilla TikZ)