asymptotes of a hyperbola

Question

Im trying to do a hyperbola with the a tangent in the middle, more or less like this, centered in x=4 and y=3

but I can get only this

the MWE is

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{datavisualization.formats.functions}
\begin{document}

\begin{tikzpicture}
  \datavisualization[
    school book axes,
    visualize as smooth line/.list={left,right},
    x axis={length=6cm, ticks and grid={major also at=4}},
    y axis={length=6cm, ticks={some}},
    data/format=function
  ]
    data[set=left] {
      var x : interval [0:3.9] samples 84;
      func y = 1 / (\value x - 4);
    }
    data[set=right] {
      var x : interval[4.1:8] samples 84;
      func y = 1 / (\value x - 4);
    };
    \addplot [mark=none,draw=violet,ultra thick,smooth,domain=0:360] {-1*tan(\x)};
\end{tikzpicture}

\end{document}  

I usually give the trigonometric functions arguments in degress, but lately it seems to work without a domain, and went well too. But this time seems not to work the tangent- The main problem is that I cant work the hyperbola to get up to y=3. Perhaps it is needs to declare the axis section, but I wonder if this will conflict with the custom definitions of the hyperbola thingys.

Answer 1

I propose the solution below. It is based on pgfplots.

• I tried to figure out the functions you are interested in from your code.
• It is a good practice to use the same technique for similar things (here the two graphs).
• It is better to give the domain for your graphs; in this way, you control what you are doing.

The code

\documentclass[border=1cm]{standalone}

\usepackage{tikz}
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    font=\scriptsize,
    axis background style={fill=gray!5},
    grid=major,
    grid style={color=gray!50},
    xtick={0,1,...,8},
    ytick={-6,-3,...,12},
    axis lines=center
    ]
    \addplot[mark=none, draw=violet, thick, smooth,
    domain=-.2:{.86+pi/2}, samples=100] {-tan(deg(x-1))};
    \addplot[mark=none, draw=violet, thick, smooth,
    domain={1.08+pi/2}:{.86+3*pi/2}, samples=100] {-tan(deg(x-1))};
    \addplot[mark=none, draw=violet, thick, smooth,
    domain={1.08+3*pi/2}:8.2, samples=100] {-tan(deg(x-1))};
    
    \addplot[mark=none, draw=red, thick, smooth, domain=-.2:3.9, samples=100]
    {1/(x-4) +3};    
    \addplot[mark=none, draw=red, thick, smooth, domain=4.1:8.2, samples=100]
    {1/(x-4) +3};    
  \end{axis}
\end{tikzpicture}

\end{document}