%
% tkz-euclide (14/01/2011)
%
% Coding (utf8) Creator (TeX) Producer (pdfeTeX) 
% Author Alain Matthes
\input{tkzfctpreamble.ltx}

\begin{document}

\begin{tikzpicture}[xscale=4,yscale=1.5]
  \tkzInit[xmin=0,xmax=3,ymax=3,ymin=-4]
  \tkzGrid(0,-4)(3,3)
  \tkzAxeXY
  \tkzClip
  \tkzVLine[color=red,style=dashed]{1/3}
  \tkzFct[color=red,domain = 0.35:3]{-3/(x*x) +4/(3*x-1)}
  \tkzFct[color=blue,domain = 0.35:3]{-3/(x*x) +27/(4*(3*x-1))}
  \tkzFct[color=orange,domain = 0.35:3]{-3/(x*x) +8/(3*x-1)}
  \tkzFct[color=green,domain = 0.35:3]{-3/(x*x) +7/(3*x-1)}
  \tkzText[draw,fill = white,text=Maroon](2,-2)%
   {$f(x)=-\dfrac{3}{x^2}+\dfrac{8\alpha}{3x-1}$ \hspace{.5cm}%
   avec $\alpha \in%
   \left\{\dfrac{1}{2}~;~\dfrac{27}{32}~;~\dfrac{7}{8}~;~1\right\}$}
\end{tikzpicture}

\end{document} 
