\documentclass[10pt]{article}
\usepackage{tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw [color=lightgray,dash pattern=on 2pt off 2pt, xstep=1.0cm,ystep=1.0cm] (-5,-5) grid (5,5);
\draw[->,color=black] (-5,0) -- (5,0);
\foreach \x in {-5,-4,-3,-2,-1,1,2,3,4}\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-5) -- (0,5);
\foreach \y in {-5,-4,-3,-2,-1,1,2,3,4}\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(-5,-5) rectangle (5,5);
\draw[smooth,samples=199,domain=-5:5] plot(\x,{2/\x});
\draw[color=black] (0.5,4.5) node[right] {$f(x)=\displaystyle\frac2x$};
\end{tikzpicture}
\end{document}
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