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

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

\begin{document}

\begin{tikzpicture}[x=1.5cm,y=3cm,xmin=-3,xmax=4,xgrille=0.5,xgrilles=0.5,ymin=-0.75,ymax=1.5,ygrille=0.25,ygrilles=0.25]
	\GrilleTikz \AxesTikz[ElargirOx=0/0,ElargirOy=0/0]
	\draw (0,0) node[below left=1pt] {$0$} ;
	\draw[thick] (1,1.75pt)--++(0,-3.5pt) node[below] {$1$} ;
	\draw[thick] (1.75pt,1)--++(-3.5pt,0) node[left] {$1$} ;
	\clip (\xmin,\ymin) rectangle (\xmax,\ymax) ;
	\draw[thick,red,samples=250,domain=\xmin:\xmax] plot (\x,{1/(1+exp(-3*\x))}) ;
	\draw[thick,blue,samples=2] plot (\x,{0.75*\x+0.5}) ;
	\filldraw (0,0.5) circle[radius=1.5pt] node[below right] {$A$} ;
	\filldraw (1,1.25) circle[radius=1.5pt] node[below right] {$B$} ;
	\draw (3.75,1.125) node[red] {$\mathcal{C}_f$} ;
	\draw (-1.25,-0.625) node[blue] {$\mathcal{T}$} ;
\end{tikzpicture}

\end{document}