Function Graph

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\documentclass[border=2pt]{standalone}
%Drawing
\usepackage{tikz}
\tikzset{>=latex}
% Notation
\usepackage{amsmath}
\begin{document}
    
    \begin{tikzpicture}
        % Grid
%       \draw[help lines] (-1,-1) grid (10,10);
        % Axis
        \draw[->, thick] (-0.2,0) -- (9,0) node[below] {$\alpha$}; 
        \draw[->, thick] (0,-0.2) -- (0,9) node[below left] {$g(\alpha)$};
        
        % Graphs
        \draw[very thick, blue, domain=0.535:8, samples=200] plot (\x,{\x^2/(\x-0.5)});
        \draw[very thick, green, domain=0:8.2, samples=200] plot (0.5,\x);
        \draw[very thick, magenta, domain=0:8, samples=200] plot (\x,{\x+0.5});
        
        % Values on Axis        
        \draw[very thick] (0.5, -3pt) -- (0.5, 3pt); 
        \node at (0.5, -0.4) {$f$};
        %   
        \draw[very thick] (-3pt, 0.5) -- (3pt, 0.5); 
        \node at (-0.3, 0.5) {$f$};
        
        % Table with Infos on the Right Corner
        \node[rounded corners, draw] at (6.5,3) {%
            \begin{tabular}{c c}
                \small$g(\alpha) = \dfrac{\alpha^2}{\alpha - f}$ & \color{blue}\textbf{–––} \\[4mm] 
                \small$y = \alpha + f$ & \color{magenta}\textbf{–––} \\[3mm] 
                \small$ x = f $ & \color{green}\textbf{–––}
            \end{tabular}};
    \end{tikzpicture}
    
\end{document}
 
 
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