\documentclass{book}
\usepackage{pgfplots}
\usepackage{amsmath}
\usepackage[%
inlinemathdigits=persian,%
displaymathdigits=persian%
]{xepersian}
\settextfont[Scale=1.2]{IRZar}
\begin{document}
\begin{center}

\begin{tikzpicture}[thick, scale=1.3,cyan]
 \begin{axis}[
 xmin=-2.5, xmax=2.5,
 ymin=-2.5, ymax=2.5,
 axis y line=center,
 axis x line=middle,
 xlabel={$x$ \text{محور}} ,ylabel={$y$ \text{محور}},
xtick=\empty,
ytick=\empty,
 ]
\addplot+[mark=none,smooth,color=magenta,domain=0:2.5] {1/(x)};
\addplot+[mark=none,smooth,color=magenta,domain=-3:0] {(-1)/(x)};
\addplot+[mark=none,smooth,color=green,domain=-2.5:0] {(x)};
\addplot+[mark=none,smooth,color=green,domain=0:2.5] {-(x)};
\addplot+[mark=none,smooth,color=blue,domain=-3:0,xshift=-.4cm, yshift=.3cm] {(-1)/(x)};
\addplot+[mark=none,smooth,color=blue,domain=0:2.5,xshift=.4cm, yshift=.3cm] {1/(x)};


 \end{axis}

 \end{tikzpicture}



\end{center}
\end{document}