% z transformée suite
\documentclass[a4paper,11pt]{article}
\usepackage[latin1]{inputenc}
\usepackage[french]{babel}
\usepackage{amsmath,amssymb}
\usepackage[left=2cm,right=1.5cm,top=2.5cm,bottom=2.5cm]{geometry}
\usepackage{fancyhdr}
\fancyhf{}
\setlength{\headheight}{26pt}
\setlength{\footskip}{18pt}
\renewcommand {\headrulewidth}{0pt}
\renewcommand {\footrulewidth}{0pt}
\usepackage{lastpage}
\pagestyle{fancy}
\usepackage {array}
\usepackage{tabularx}
\usepackage{pstricks,pst-all,pstricks-add,pst-tree,pst-3dplot,pst-circ}
%\usepackage{setspace}
\usepackage{dsfont}
\usepackage[np]{numprint}
\usepackage{graphicx}
\usepackage{eso-pic} % pour avoir un trait de marge vertical
\usepackage{multicol}
\usepackage [alwaysadjust]{paralist}
\usepackage{colortbl}
\usepackage{eurosym}
\usepackage{spreadtab} % pour une tabulation automatique
%\usepackage{enumitem} % pour des puces différentes dans des listes
\usepackage{enumerate}
\frenchbsetup{StandardLists=true} % pour des points au lieu des tirets pour les listes par défaut

\setdefaultenum {1.}{a)}{}{}
\hyphenpenalty 10000 % empèche la coupure de mots
\renewcommand*{\tabularxcolumn}[1]{m{#1}} %centrage vertical des cellules d'un tableau tabularx

\newcommand{\R}{\mathds {R}}
\newcommand{\N}{\mathds {N}}
\newcommand{\Z}{\mathds {Z}}
\newcommand{\Q}{\mathds {Q}}
\newcommand{\C}{\mathds {C}}

\newcommand{\vect}[1]{\mathchoice%
{\overrightarrow{\displaystyle\mathstrut#1\,\,}}%
{\overrightarrow{\textstyle\mathstrut#1\,\,}}%
{\overrightarrow{\scriptstyle\mathstrut#1\,\,}}%
{\overrightarrow{\scriptscriptstyle\mathstrut#1\,\,}}}

\renewcommand{\theenumi}{\textbf{\arabic{enumi}}}
\renewcommand{\labelenumi}{\textbf{\theenumi.}}
\renewcommand{\theenumii}{\textbf{\alph{enumii}}}
\renewcommand{\labelenumii}{\textbf{\theenumii.}}

\def\Oij{$\left(\text{O},~\vect{i},~\vect{j}\right)$}
\def\Ouv{$\left(\text{O},~\vect{u},~\vect{v}\right)$}
\def\ds{\displaystyle }
\def\tvi{\vrule height 15pt depth 10pt width 0pt }

\DecimalMathComma

% ########################### MES PARAMETRES ##############################################################
\def\monnumero{ 01 }
\def\madate{ Octobre 2023}
% ########################### MES PARAMETRES ##############################################################

% en-tete
\lhead{\footnotesize{\textsf{Lycée Schuman Perret\\ \madate}}} %gauche
\chead{\textsf{\textcolor{red}{\textbf{\textsc{série d'exercices No\monnumero}}}}} %centre
\rhead{\footnotesize{\textsf{Cira 2 }}}%droit
%pied de page
\rfoot{\scriptsize{\textsf{Page~\thepage{}~sur~\pageref{LastPage}}}}
\lfoot{\scriptsize{\textsf{\textsc{Stéphane Le Méteil }}}}

\setlength{\columnseprule}{0.5pt}
\setlength{\columnsep}{30pt}
\setlength{\parindent}{0mm}

\newcounter{nexo}\setcounter{nexo}{0}
\newcommand{\exo}{\bigskip  \stepcounter{nexo} \vskip 0.3cm \par{\textsf{\textbf{\textcolor{blue}{{\small{EXERCICE~\arabic{nexo}}}}}}}\quad}
\def\taille{\vrule height 25pt depth 20pt width 0pt }

\usepackage{paralist}

\newlength{\positionbarre}
\setlength{\positionbarre}{1.7 cm}% à changer selon les besoin
\AddToShipoutPicture{%
\put(\LenToUnit{\positionbarre},\LenToUnit{0.05\paperheight}){\begin{picture}(0,0)(0,0) \color{red}\line(0,1){\LenToUnit{0.85\paperheight}}\end{picture}}
}
\makeatother

\begin{document}%\everymath{\displaystyle}
\setdefaultleftmargin{0.6cm}{0.5cm}{}{}{}{}

\exo Dessiner une fonction.

\begin{enumerate}
\item A base d'échelon.

    \begin{enumerate}
      \item $U(t) = \left\{\begin{matrix}1&\text{ si } t\geqslant 0\cr 0&\text{ sinon }\end{matrix}\right.$
      \item $f(t) = U(t-1)$
      \item $f(t) = 2U(t)$
      \item $f(t) = U(t)-U(t-2)$
      \item $f(t) = U(t)-U(t-\frac{\pi}{3})-U(t-\frac{2\pi}{3})+U(t-\pi)$
      \item $f(t) = \sin(t) \times \Big(U(t)-U(t-\pi)\Big)$
    \end{enumerate}

\item A base de rampe.

    \begin{enumerate}
      \item $f(t) = t\times U(t)$
      \item $f(t) = (t-2)\times U(t-2)$
      \item $f(t) = 2\times t\times U(t)$
      \item $f(t) = t\times U(t) - (t-2)\times U(t-2)$
      \item $f(t) = t\times U(t) - 2(t-1)\times U(t-1)$
      \item $f(t) = t\times U(t) - 2(t-1)\times U(t-1) + (t-2)\times U(t-2)$
      \item $f(t) = t\times ( U(t) - U(t-2) )$
      \item $f(t) = t\times U(t-1)$
      \item $f(t) = t\times  U(t) - U(t-1)$
    \end{enumerate}

\end{enumerate}

\exo Reconnaître un graphe

a)\begin{pspicture*}(-2.76,-0.82)(4.68,2.68)
\multips(0,0)(0,1.0){4}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(-2.76,0)(4.68,0)}
\multips(-2,0)(1.0,0){8}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(0,-0.82)(0,2.68)}
\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-2.76,-0.82)(4.68,2.68)
\psline[linewidth=2.pt](-4.,0.)(1.,0.)(1.,2.)(6.28,1.98)
\end{pspicture*}
\hfill
b)\begin{pspicture*}(-2.76,-0.82)(4.68,2.68)
\multips(0,0)(0,1.0){4}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(-2.76,0)(4.68,0)}
\multips(-2,0)(1.0,0){8}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(0,-0.82)(0,2.68)}
\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-2.76,-0.82)(4.68,2.68)
\psline[linewidth=2.pt](-4.,0.)(1.,0.)(1.,2.)(2,2)(2,0)(4.48,0)
\end{pspicture*}

\bigskip

c)\begin{pspicture*}(-2.76,-0.82)(4.68,2.68)
\multips(0,0)(0,1.0){4}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(-2.76,0)(4.68,0)}
\multips(-2,0)(1.0,0){8}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(0,-0.82)(0,2.68)}
\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-2.76,-0.82)(4.68,2.68)
\psline[linewidth=2.pt](-4.,0.)(1.,0.)(3,2)(4.48,2)
\end{pspicture*}
\hfill
d)\begin{pspicture*}(-2.76,-0.82)(4.68,2.68)
\multips(0,0)(0,1.0){4}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(-2.76,0)(4.68,0)}
\multips(-2,0)(1.0,0){8}{\psline[linestyle=dashed,linecap=1,dash=1.5pt 1.5pt,linewidth=0.4pt,linecolor=lightgray]{c-c}(0,-0.82)(0,2.68)}
\psaxes[labelFontSize=\scriptstyle,xAxis=true,yAxis=true,Dx=1.,Dy=1.,ticksize=-2pt 0,subticks=2]{->}(0,0)(-2.76,-0.82)(4.68,2.68)
\psline[linewidth=2.pt](-4.,0.)(0.,0.)(1.,2.)(2,2)(3,0)(4.48,0)
\end{pspicture*}


\end{document}