%!tikz editor 1.0
\documentclass{article}
\usepackage{tikz}
\usepackage[graphics, active, tightpage]{preview}
\usepackage{circuitikz}
\PreviewEnvironment{tikzpicture}

%!tikz preamble begin
\usepackage{pgfplots}
%!tikz preamble end


%%%%%%%%%
%%   convert -density 300 GW001.pdf -quality 100 GW001.png
%%%%%%%%%

\begin{document}
%!tikz source begin
\begin{tikzpicture}
[line cap=round,line join=round,x=1cm,y=1cm,scale=1]
\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=-0.1,
ymax=2.5,
ytick=\empty,
xtick=\empty,
xlabel=$x$,
ylabel=$y$,
extra x ticks  = {0.75, 1.25,1.75,2.25},
extra x tick labels= {$x_0$,  $x_3$, $x_2$, $x_1$},
extra y ticks  = {0.71232, 1.22314, 1.55962, 1.81093},
extra y tick labels= {$g_r$,  $f(x_3)$, $f(x_2)$, $f(x_1)$}
]

%\addplot[domain=-2.7:-1.1, blue, line width=1,samples=500] {1/(x^2-1)}; 
%\addplot[domain=1.1:2.7, blue, line width=1,samples=500] {1/(x^2-1)}; 
\addplot[domain=0.75:2.65, blue, line width=1,samples=500] {1+ln(x)}; 


\addplot[color=blue, only marks, fill=white] coordinates {(0.75,0.71232)};

\draw [dashed, blue] (axis cs: 0.75,-0.05) -- (axis cs: 0.75,0.71232);

\draw [dashed, blue] (axis cs: -0.05,0.71232) -- (axis cs: 0.75,0.71232);

\addplot[color=blue, only marks] coordinates {(1.25,1.22314)};


\draw [ blue, thin] (axis cs: 1.25,0) -- (axis cs: 1.25,1.22314);

\draw [ blue, thin] (axis cs: 0, 1.22314) -- (axis cs: 1.25,1.22314);

\addplot[color=blue, only marks] coordinates {(1.75,1.55962)};

\draw [ blue, thin] (axis cs: 1.75,0) -- (axis cs: 1.75,1.55962);

\draw [ blue, thin] (axis cs: 0, 1.55962) -- (axis cs: 1.75,1.55962);

\addplot[color=blue, only marks] coordinates {(2.25,1.81093)};


\draw [ blue, thin] (axis cs: 2.25,0) -- (axis cs: 2.25,1.81093);

\draw [ blue, thin] (axis cs: 0, 1.81093) -- (axis cs: 2.25,1.81093);

\end{axis}


\end{tikzpicture}
%!tikz source end

\end{document}