\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
\tikzset{
        every pin/.style={fill=yellow!50!white,rectangle,rounded corners=3pt,font=\tiny},
        small dot/.style={fill=black,circle,scale=0.3},}
\begin{axis}[
x=2cm,y=2cm,
axis lines=middle,
axis line style = {-latex},
xmin=-0.5,
xmax=3,
ymin=-0.5,
ymax=2,
ytick=\empty,
xtick=\empty,
xlabel=$x$,
ylabel=$y$,
extra x ticks={1.3},
    extra x tick style={
        tick label style={anchor=north}},
    extra x tick labels={$x_0$},
 extra y ticks={1.14},
 extra y tick style={
        tick label style={anchor=east}},
    extra y tick labels={$\displaystyle \sqrt{x_0}$},
enlargelimits = true,
]
  \draw [thick, dashed] 
        (axis cs: -0.05,1.14) -- (axis cs: 1.3,1.14);
  \draw [thick, dashed] 
        (axis cs: 1.3,-0.05) -- (axis cs: 1.3,1.14);
\node[label={180:{}},circle,fill,inner sep=1.5] at (axis cs:1.3,1.14) {};
\node[label={300:{$0$}},circle,fill,inner sep=1.5] at (axis cs:0,0) {};
 %       node[pos=0.5, above] {$y=12$};
 %  \addplot coordinates { (0,1.14) (1.3,1.14) };
 %   \addplot coordinates { (1,4) (2,6) };
  %  \draw (axis cs:2,3) -- node[left]{Text} (axis cs:2,6);

\addplot[domain=0:2, blue, line width=1,samples=5000] {sqrt(x)};
%\addplot[domain=-3.8:-0.05, red,  line width=1,samples=5000] {sin(deg(1/(x)))};


\begin{scriptsize}
 \node () at (axis cs:2.2,1.7) {$\displaystyle y=\sqrt{x}\;(x \neq 0)$};
\end{scriptsize}

% \draw[] (axis cs:1.3, 0.1) -- (axis cs:1.3, -0.1);
% \node () at (axis cs:1.3,-0.25) {$x_0$};

% \draw[] (axis cs:1.14,-0.05) -- (axis cs:1.14, 0.05);
% \node () at (axis cs:0.33,-0.45) {$\frac{1}{\pi}$};

\end{axis}



\end{tikzpicture}