Cfrgtkky

I'm trying to plot vertical asymptotes in my graph but I can't.

This is my code:

documentclass[a4paper]{article}

usepackage{pgfplots}

usepackage{amsmath}

begin{document}

begin{center}

begin{tikzpicture}

begin{axis}%

[

    grid=major,  

    x=5mm,

    y=5mm,

    xtick={-15,-14,...,15},   

    xmin=-15,

    xmax=15,

    xlabel={tiny $x$},

    axis x line=middle,

    ytick={-8,-7,...,8},

    tick label style={font=tiny},

    ymin=-8,

    ymax=8,

    ylabel={scriptsize $ qquad qquad qquad f(x)=dfrac{x^2-4*x-5}{x^2-9}$},

    axis y line=middle,

    no markers,

    samples=100,

    domain=-15:15,

    restrict y to domain=-10:10

]

addplot[thick,samples=800] (x,{(x^2-4*x-5)/(x^2-9});

addplot[thick,dashed, samples=800] (x,1);

draw[dashed] ( -3,-8) -- ( -3,+8);

draw[dashed] ( 3,-8) -- ( 3,+8);

 end{axis} 

end{tikzpicture}

end{center}

end{document}

The issue is that you do not specify the compatibility version, so pgfplots runs in backwards mode. If you want to keep that, you need to add axis cs: to the coordinates in the draw mode. It is arguably simpler and better to specify a reasonably new version.

documentclass[a4paper]{article}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

usepackage{amsmath}

begin{document}

begin{center}

begin{tikzpicture}

begin{axis}%

[

    grid=major,  

    x=5mm,

    y=5mm,

    xtick={-15,-14,...,15},   

    xmin=-15,

    xmax=15,

    xlabel={tiny $x$},

    axis x line=middle,

    ytick={-8,-7,...,8},

    tick label style={font=tiny},

    ymin=-8,

    ymax=8,

    ylabel={scriptsize $ qquad qquad qquad f(x)=dfrac{x^2-4*x-5}{x^2-9}$},

    axis y line=middle,

    no markers,

    samples=100,

    domain=-15:15,

    restrict y to domain=-10:10

]

addplot[thick,samples=800] (x,{(x^2-4*x-5)/(x^2-9});

addplot[thick,dashed, samples=800] (x,1);

draw[dashed] ( -3,-8) -- ( -3,+8);

draw[dashed] ( 3,-8) -- ( 3,+8);

end{axis} 

end{tikzpicture}

end{center}

end{document}

If you need to run pgfplots in backwards compatibility mode, you could use

documentclass[a4paper]{article}

usepackage{pgfplots}

usepackage{amsmath}

begin{document}

begin{center}

begin{tikzpicture}

begin{axis}%

[

    grid=major,  

    x=5mm,

    y=5mm,

    xtick={-15,-14,...,15},   

    xmin=-15,

    xmax=15,

    xlabel={tiny $x$},

    axis x line=middle,

    ytick={-8,-7,...,8},

    tick label style={font=tiny},

    ymin=-8,

    ymax=8,

    ylabel={scriptsize $ qquad qquad qquad f(x)=dfrac{x^2-4*x-5}{x^2-9}$},

    axis y line=middle,

    no markers,

    samples=100,

    domain=-15:15,

    restrict y to domain=-10:10

]

addplot[thick,samples=800] (x,{(x^2-4*x-5)/(x^2-9});

addplot[thick,dashed, samples=800] (x,1);

draw[dashed] (axis cs: -3,-8) -- (axis cs: -3,+8);

draw[dashed] (axis cs: 3,-8) -- (axis cs: 3,+8);

end{axis} 

end{tikzpicture}

end{center}

end{document}

which yields the same output. However, I would like to argue it is better to update the TeX installation because, apart from adding features, some real bugs have been fixed.