Function Graph

Edit and compile if you like:

\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}