Modifié le 22 Octobre 2006 à 20 h 49.
%@P:exocorcp
%@metapost:3affineexo44.mp
\opcopy{-2.2}{a}
\opset{decimalsepsymbol={,}}
\begin{center}
\psshadowbox{
\begin{minipage}{0.75\linewidth}
La représentation graphique d'une fonction $f$ est l'ensemble de tous
les points $M$ de coordonnées $(x;f(x))$ obtenus en prenant toutes les
valeurs possibles du nombre $x$.
\end{minipage}
}
\end{center}
On se propose de représenter graphiquement la fonction $f$ définie par
\[x\mapsto x^2-x-1\]
\begin{myenumerate}
\item Recopie et complète les tableaux suivants :
\begin{center}
\begin{tabular}{|c|*{9}{m{1cm}|}}
\hline
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}\\
\hline
$f(x)$&&&&&&&&&\\
\hline
\end{tabular}
\end{center}
\opcopy{-0.3}{a}
\begin{center}
\begin{tabular}{|c|*{9}{m{1cm}|}}
\hline
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}\\
\hline
$f(x)$&&&&&&&&&\\
\hline
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{|c|*{9}{m{1cm}|}}
\hline
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}\\
\hline
$f(x)$&&&&&&&&&\\
\hline
\end{tabular}
\end{center}
\item Place tous ces points dans un repère.
\end{myenumerate}
%@Correction:
\opcopy{-2.2}{a}
\opcopy{-2.2}{b}
\opset{decimalsepsymbol={,}}
\begin{center}
\begin{tabular}{|c|*{9}{m{1cm}|}}
\hline
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}\\
\hline
$f(x)$&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}\\
\hline
\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}\\
\hline
\opcopy{-0.3}{a}
\opcopy{-0.3}{b}
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,2}{a}$\opprint{a}$}\\
\hline
$f(x)$&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,2}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}\\
\hline
\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}&\multicolumn{1}{m{1cm}}{}\\
\hline
$x$&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}&\multicolumn{1}{c|}{\opadd*{a}{0,1}{a}$\opprint{a}$}\\
\hline
$f(x)$&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}&\multicolumn{1}{c|}{\opadd*{b}{0,1}{b}\opmul*{b}{b}{c}\opsub*{c}{b}{c}\opsub*{c}1{c}\opprint{c}}\\
\hline
\end{tabular}
\end{center}
\[\includegraphics{3affineexo44.1}\]