\begin{exercice*}[~\hfill\ExerciceRefMethode{meth_conti_fonction}]\label{exo_meth_conti_fonction}
Dans chaque repère ci-dessous, la courbe tracée \mbox{représente} une fonction $f$.
\begin{enumerate}
\item Déterminer les intervalles où $f$ est continue.
\item Donner l'image de $1$ par la fonction $f$.\par
Coïncide-t-elle avec les limites de $f$ en 1, à gauche et à droite ?
\end{enumerate}\vspace{2mm}
\begin{ChoixQCM}{2}
\item \begin{minipage}{\linewidth}
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true}
\begin{pspicture*}(-1.2,-0.7)(3.2,2.3)
\psgrid[subgriddiv=2,linewidth=0.5pt,gridcolor=A3,subgridcolor=A3,gridlabels=0pt](0,0)(-2,-3)(4,3)
\psaxes[linewidth=0.8pt,Dx=1,Dy=1,ticksize=-2pt]{->}(0,0)(-1.2,-2.3)(3.2,2.3)
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{-1.}{0}{sqrt(x*(x-1)/2)}
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{1}{3}{x-1}
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{0}{1}{-abs(x-0.5)+0.5}
\rput[0](-1,1){\textcolor{Blanc}{$\scriptstyle\bullet$}} \rput[0](-1,1){\textcolor{red}{$\scriptstyle\circ$}}
\rput[0](3,2){\textcolor{Blanc}{$\scriptstyle\bullet$}} \rput[0](3,2){\textcolor{red}{$\scriptstyle\circ$}}
\end{pspicture*}
\end{minipage}
\item \begin{minipage}{\linewidth}
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true}
\begin{pspicture*}(-1.2,-2.3)(3.2,2.3)
\psgrid[subgriddiv=2,linewidth=0.5pt,gridcolor=A3,subgridcolor=A3,gridlabels=0pt](0,0)(-2,-3)(4,3)
\psaxes[linewidth=0.8pt,Dx=1,Dy=1,ticksize=-2pt]{->}(0,0)(-1.2,-2.3)(3.2,2.3)
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{-1.}{1}{x^2}
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{1}{3.}{2-x}
\rput[0](1,0){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](-1,1){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](3,-1){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](1,1){\textcolor{Blanc}{$\scriptstyle\bullet$}}
\rput[0](1,1){\textcolor{red}{$\scriptstyle\circ$}}
\end{pspicture*}
\end{minipage}
\item \begin{minipage}{\linewidth}
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true}
\begin{pspicture*}(-1.2,-0.7)(3.2,2.3)
\psgrid[subgriddiv=2,linewidth=0.5pt,gridcolor=A3,subgridcolor=A3,gridlabels=0pt](0,0)(-2,-3)(4,3)
\psaxes[linewidth=0.8pt,Dx=1,Dy=1,ticksize=-2pt]{->}(0,0)(-1.2,-2.3)(3.2,2.3)
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{-1.}{0}{sqrt(x*(x-1)/2)}
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{1}{3}{x-1}
%\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{0}{1}{-abs(x-0.5)+0.5}
\rput[0](-1,1){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](3,2){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](1,0){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](0,0){\textcolor{Blanc}{$\scriptstyle\bullet$}} \rput[0](0,0){\textcolor{red}{$\scriptstyle\circ$}}
\end{pspicture*}
\end{minipage}
\item \begin{minipage}{\linewidth}
\psset{xunit=0.8cm,yunit=0.8cm,algebraic=true}
\begin{pspicture*}(-1.2,-2.3)(3.2,2.3)
\psgrid[subgriddiv=2,linewidth=0.5pt,gridcolor=A3,subgridcolor=A3,gridlabels=0pt](0,0)(-2,-3)(4,3)
\psaxes[linewidth=0.8pt,Dx=1,Dy=1,ticksize=-2pt]{->}(0,0)(-1.2,-2.3)(3.2,2.3)
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{-1.}{1}{x^2}
\psplot[linecolor=red,plotpoints=5000,linewidth=0.8pt]{1}{3}{2-(x-1)^2}
\rput[0](-,1){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](3,-2){\textcolor{red}{$\scriptstyle\bullet$}}
\rput[0](1,1){\textcolor{red}{$\scriptstyle\bullet$}} 
\rput[0](1,2){\textcolor{Blanc}{$\scriptstyle\bullet$}} \rput[0](1,2){\textcolor{red}{$\scriptstyle\circ$}}
\end{pspicture*}
\end{minipage}
\end{ChoixQCM}
 \begin{corrige}
  \begin{enumerate}
  \item  \reponseQCM{a} $]-1~;~3[$  
  \reponseQCM{b} $[-1~;~1[$ et $]1~;~3[$
  \reponseQCM{c} $[-1~;~0[$ et $[1~;~3]$
  \reponseQCM{d} $[-1~;~1]$ et $]1~;~3[$
  \item  \reponseQCM{a} $f(1)=0$ ; $\displaystyle\lim_{\substack{x\to 1\\ x<1}}f(x)=\displaystyle\lim_{\substack{x\to 1\\ x>1}}f(x)=0$.
  \reponseQCM{b} $f(1)=0$ ; $\displaystyle\lim_{\substack{x\to 1\\ x<1}}f(x)=\displaystyle\lim_{\substack{x\to 1\\ x>1}}f(x)=1$.
  \reponseQCM{c} $f(1)=0$ ; $\displaystyle\lim_{\substack{x\to 1\\ x<1}}f(x)$ n'existe pas  et $\displaystyle\lim_{\substack{x\to 1\\ x>1}}f(x)=0$.
  \reponseQCM{d} $f(1)=1$ ; $\displaystyle\lim_{\substack{x\to 1\\ x<1}}f(x)=1$ et $\displaystyle\lim_{\substack{x\to 1\\ x>1}}f(x)=2$.
  \end{enumerate}
\end{corrige}
\end{exercice*}

