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+ \begin{solution} + D'après le tableau de variations, la fonction $f$ est décroissante sur $\intFF{-2}{0} \cup \intFF{1}{2}$. + \end{solution} + %1pt + \item Déterminer le maximum de la fonction sur l'intervalle $\intFF{-4}{4}$. + \begin{solution} + Sur l'intervalle $_intFF{-4}{4}$ (l'intervalle de définition de $f$), le maximum est atteint pour $x = 4$ et vaut $f(4) = 3$. + \end{solution} + \item Comparer $f(0,2)$ et $f(0,5)$. + %1pt + \item Tracer une fonction qui a ce tableau de variation. + \begin{solution} + Voici une courbe possible + \begin{center} + \begin{tikzpicture}[scale=0.8] + \repere{-6}{6}{-6}{6} + \draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{% + (-4, -4) (-2,1) (0,-3) (1,0) (2,-3) (4,3) + }; + \draw (4,3) node[above right] {$\mathcal{C}_f$}; + \end{tikzpicture} + \end{center} + \end{solution} + \end{enumerate} + + \item Voici la représentation graphique de la fonction $g$. + + \hspace{-1cm} + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture}[scale=0.7] + \repere{-5}{5}{-5}{5} + \draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{% + (-4, -4) (-3.5, 0) (-3, 4) (-2, 1) (-1, 0) (0, -1) (1, -2) (2, 1) (3, 3) (4, 2)% + }; + \draw (4,3) node[above right] {$\mathcal{C}_g$}; + + \end{tikzpicture} + \begin{solution} + \begin{center} + \begin{tikzpicture}[scale=0.8] + \repere{-5}{5}{-5}{5} + \draw[very thick, color=red] plot [smooth,tension=0.5, mark=*] coordinates{% + (-4, -4) (-3.5, 0) (-3, 4) (-2, 1) (-1, 0) (0, -1) (1, -2) (2, 1) (3, 3) (4, 2)% + }; + \draw (4,3) node[above right] {$\mathcal{C}_g$}; + + \ifprintanswers + \draw[color = blue, dashed, very thick] (3,0) node[below] {3} -- (3,3) -- (0,3) node[left] {$f(3)$}; + + \draw[color=green, dashed, very thick] (-6,1) -- (6,1) node [above] {$y=1$}; + \draw[color=green, dashed, very thick] (-3.4,1) node {$\bullet$} -- (-3.4,0) node [below] {-3,4}; + \draw[color=green, dashed, very thick] (-2,1) node {$\bullet$} -- (-2,0) node [below] {-2}; + \draw[color=green, dashed, very thick] (2,1) node {$\bullet$} -- (2,0) node [below] {2}; + \fi + \end{tikzpicture} + \end{center} + \end{solution} + \end{minipage} + \begin{minipage}{0.6\textwidth} + \begin{enumerate} + % O.5pt + \item Quel est l'image de 3 par cette fonction? Vous laisserez les traits de construction qui vous ont permis de répondre. + \begin{solution} + L'image de 3 par la fonction $g$ est 3. Voir les traits en bleu. + \end{solution} + % O.5pt + \item Quels sont les antécédents de 1 par cette fonction? Vous laisserez les traits de construction qui vous ont permis de répondre. + \begin{solution} + Les antécédents de 1 par cette fonction sont 2, -2 et environ -3,4. Voir les traits en vert. + \end{solution} + %2pts + \item Tracer le tableau variation de $f$. + \begin{solution} + Tableau de variation de cette fonction + \begin{tikzpicture} + \tkzTabInit[espcl=2]{$x$/1,$f(x)$/1}{-4, -3, 1, 3, 4} + \tkzTabVar{-/{-4}, +/{4}, -/{-2}, +/{3}, -/{2}, } + \end{tikzpicture} + \end{solution} + \item Combien y a-t-il de solutions à l'équation $g(x) = 3$? + \item Résoudre graphiquement $g(x) < -1$ + \end{enumerate} + \end{minipage} + \end{enumerate} +\end{exercise} + + +\end{document}