\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}
\begin{center}
\begin{tikzpicture}[ scale=2,radius=1pt,domain=0:4]
\draw [<-,thick] (0,2) node(yline)[left]{$m$} -- (0,0) ;
\draw [->,thick] (0,0) -- (4,0) ;
    \draw (.5 cm,1pt) -- (.5 cm,-1pt) node[anchor=north] {$a$};
    \draw (3 cm,1pt) -- (3 cm,-1pt) node[anchor=north] {$x_0$};
    \draw (3.5 cm,1pt) -- (3.5 cm,-1pt) node[anchor=north] {$b$};
    \draw (1pt, .5cm) -- (-1pt,.5cm) node[left] {$k$};
%  \draw [-,thick] (.5,1.75)  to [out=-70,in=140] (1,1.5) to [out=-45,in=150] (1.75,1.75) to [out=-55,in=50] (3,.5) to [out=50,in=100] (3.5,1) ;
\draw (.5,1.75) .. controls (1,1.5) and (1.75,1.75) .. (3,.5)  ;
\end{tikzpicture}
\end{center}
\end{document}