# Drawing functions [duplicate]

How do I draw this function on Tikz or any other alternative??

You can use pgfplots with unbounded coords=jump. Then you can use a function that has the right poles and asymptotics, and plot it. It is usually a good idea to keep the number of samples odd for a symmetric function.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}
\begin{tikzpicture}[declare function = {f(\x)=4-8*\x*\x/((\x-3)*(\x+3));}]
\begin{axis}[width=10cm,axis lines=center,unbounded coords=jump,
xlabel=$x$,xlabel style={anchor=north east},
xtick=\empty,ytick=\empty,
ylabel=$y$,
ymin=-12,ymax=12,xmin=-10,xmax=10
]
\path (-3,0) node[below left] {$-3$} (3,0) node[below right] {$3$}
(0,4) node[below right] {$4$} (0,-4) node[below right] {$-4$}
(0,0) node[below left] {$O$};
\end{axis}
\end{tikzpicture}
\end{document}


An example can be:

\documentclass[margin=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
declare function = {f(\t)=(6*(\t)^2-3*\t+4)/(2*(\t)^2-8);},
axis lines = center,
xlabel = $x$,
xlabel style = {anchor=north east},
ylabel = $y$,
ymin = -100, ymax = 100,
]
\addplot [red, thick, domain=-5:5, samples=400] {f(x)};
\end{axis}
\end{tikzpicture}
\end{document}


For shoved graph you only need to replace declare function = ... with function which you like to show.