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a/2nd/03_Fonctions_et_graphiques/exercises.tex b/2nd/03_Fonctions_et_graphiques/exercises.tex index 6675b9a..ae11eec 100644 --- a/2nd/03_Fonctions_et_graphiques/exercises.tex +++ b/2nd/03_Fonctions_et_graphiques/exercises.tex @@ -109,11 +109,11 @@ \begin{tikzpicture}[yscale=0.4, xscale=0.6] %\repere{-9}{4}{-5}{4} \tkzInit[xmin=-9,xmax=4,xstep=1, - ymin=-5,ymax=4,ystep=1] + ymin=-4,ymax=5,ystep=1] \tkzGrid \tkzAxeXY \draw[very thick, color=red] plot [smooth,tension=0.2] coordinates{% - (-8,0.2) (-6,3) (-2,-4.5) (0,-2) (1,0) (3,1.5) + (-8,-0.2) (-6,-3) (-2,4.5) (0,2) (1,0) (3,-1.5) }; \draw (3,1) node[above right] {$\mathcal{C}_f$}; \end{tikzpicture} @@ -142,36 +142,52 @@ \end{exercise} \begin{exercise}[subtitle={Lecture graphique}, step={4}, origin={???}, topics={ Fonctions et graphiques }, tags={ Fonctions, Graphiques }] - \begin{minipage}{0.5\textwidth} - \begin{tikzpicture}[xscale=0.7, yscale=0.6] - \tkzInit[xmin=-6,xmax=6,xstep=1, - ymin=-3,ymax=3,ystep=1] - \tkzGrid - \tkzAxeXY - \draw (4,2) node[below left] {$\mathcal{C}_g$}; - \tkzFct[domain = -6:6,color=red,very thick]% - {0.05*(x+5)*(x+1)*(x-4)} + Sur le graphique ci-dessous, on tracer les représentations graphiques des fonctions + \[ + f(x) = 0.05(x+5)(x+1)(x-4) \qquad g(x) = 0.1x^2 - 1 + \] + \begin{minipage}{0.4\textwidth} + \begin{tikzpicture} + \begin{axis}[ + axis lines = center, + grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=1, + legend pos = north west, + legend entries={$f(x)$, $g(x)$} + ] + \addplot[domain=-6:6,samples=20, color=red, very thick]{0.05*(x+5)*(x+1)*(x-4)}; + \addplot[domain=-6:6,samples=20, color=blue, very thick]{0.1*x^2 - 1}; + \end{axis} \end{tikzpicture} \end{minipage} - \begin{minipage}{0.5\textwidth} + \begin{minipage}{0.6\textwidth} \begin{enumerate} \item Résoudre graphiquement les équations suivantes \begin{multicols}{2} \begin{enumerate} - \item $g(x) = 1,5$ - \item $g(x) = -2$ - \item $g(x) = 3$ + \item $g(x) = 0$ + \item $f(x) = 2$ + + \item $0.1x^2 - 1 = -1$ + \item $f(x) = g(x)$ \end{enumerate} \end{multicols} \item Résoudre graphiquement les inéquations suivantes - \begin{multicols}{2} + \begin{multicols}{3} \begin{enumerate} \item $g(x) \geq 0$ - \item $g(x) < -1,5$ - \item $g(x) > 1 $ + \item $f(x) \leq 2$ + \item $g(x) > f(x)$ \end{enumerate} \end{multicols} + \begin{enumerate} + \setcounter{enumii}{3} + \item $0.05(x+5)(x+1)(x-4) > 1 $ + \end{enumerate} \end{enumerate} \end{minipage} \end{exercise}