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\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N° 13164286510338--
%%--Axe de symétrie et centre de symétrie d\'une courbe--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%


\begin{exercise}%
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La courbe $\mathcal{C}$ ci-contre a pour équation\newline$y=x^{2}-2x-1$ dans
le repère $\left(  O;\overrightarrow{i};\overrightarrow{j}\right)  .$

\begin{enumerate}
\item Conjecturer un axe de symétrie pour $\mathcal{C}.$

\item Choisir un point $A$ sur cette axe comme origine d'un nouveau repère
$\left(  A;\overrightarrow{i};\overrightarrow{j}\right)  $ et écrire les
formules de changement de repère.

\item Établir la nouvelle équation $Y=g(X)$ de $\mathcal{C}$ dans le repère
$\left(  A;\overrightarrow{i};\overrightarrow{j}\right)  $ et démontrer votre conjecture.
\end{enumerate}

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\item On considère la fonction $f$ définie par:%
\[
f(x)=\frac{x-1}{x^{2}-2x-2}.
\]


\begin{enumerate}
\item Déterminer l'ensemble de définition $\mathcal{D}_{f}$ de $f;$

\item Démontrer que $I(1;0)$ est centre de symétrie de $\mathcal{C}_{f}.$
\end{enumerate}
\end{exercise}


\end{document}