% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage{ProfLycee}

\begin{document}

\begin{tikzpicture}[x=0.8cm,y=0.8cm,xmin=-7,xmax=8,xgrille=1,xgrilles=0.5,ymin=-2,ymax=6,ygrille=1,ygrilles=0.5]
	\GrilleTikz \AxesTikz[ElargirOx=0/0,ElargirOy=0/0]
	\AxexTikz[Police=\footnotesize]{-7,-6,...,7}
	\AxeyTikz[Police=\footnotesize]{-2,-1,...,5}
	\clip (\xmin,\ymin) rectangle (\xmax,\ymax) ;
	\draw[line width=1.25pt,red,domain=\xmin:\xmax,samples=250] plot (\x,{ln(\x*\x+1)+3-ln(2)}) ;
	\draw[red] (-5.5,5.75) node[below,font=\large] {$\mathcal{C}_f$} ;
	\draw[line width=1.25pt,domain=\xmin:\xmax,samples=2,dashed] plot (\x,{\x+2}) ;
	\draw[fill=black] (1,3) circle[radius=1.75pt] node[below right] {$A$} (3,5) circle[radius=1.75pt] node[above left] {$B$} ;
\end{tikzpicture}

\end{document}