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b/3e/Gestion_donnees/Generalite_fonctions/E3_fonctions_numeriques.tex new file mode 100644 index 0000000..dc2d33f --- /dev/null +++ b/3e/Gestion_donnees/Generalite_fonctions/E3_fonctions_numeriques.tex @@ -0,0 +1,58 @@ +\documentclass[a5paper,10pt]{article} +\usepackage{myXsim} + +\title{Images et antécédents de fonctions} +\tribe{Troisième} +\date{Juin 2018} + +\pagestyle{empty} +\geometry{left=10mm,right=10mm, top=10mm} + +\begin{document} +\begin{exercise}[subtitle={Fonctions en tout genre}] + + \paragraph{Tableau de valeurs}~\\ + \vfill + \begin{tabular}{|c|*{9}{c|}} + \toprule + x & -5 & -4.5 & -4 & -3.5 & -3 & -2.5 & -2 & -1.5 & -1 \\ + \midrule + f(x) & 10.5 & 8.125 & 6 & 4.125 & 2.5 & 1.125 & 0 & -0.875 & -1.5 \\ + \bottomrule + \end{tabular} + + \vfill + + \paragraph{Représentation graphique}~\\ + \vfill + \begin{center} + \begin{tikzpicture}[scale=1] + \tkzInit[xmin=-5,xmax=5,xstep=1,ymax=3,ymin=-3,ystep=1] + \tkzAxeX[right, very thick] + \tkzAxeY[above, very thick] + \tkzGrid + \tkzFct[color=red, very thick]{2*x**2/(x**2+1)} + \tkzText(4.2,2.2){$g$} + \end{tikzpicture} + \end{center} + + \vfill + \paragraph{Formule}~\\ + \vfill + \[ + h:x \mapsto 2x + 2 + \] + \vfill + \[ + i(x) = 2x^2 - 3x + 1 + \] + \vfill + +\end{exercise} +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "master" +%%% End: + diff --git a/3e/Gestion_donnees/Generalite_fonctions/index.rst b/3e/Gestion_donnees/Generalite_fonctions/index.rst index 9ab944d..b0a3ec3 100644 --- a/3e/Gestion_donnees/Generalite_fonctions/index.rst +++ b/3e/Gestion_donnees/Generalite_fonctions/index.rst @@ -2,7 +2,7 @@ Généralités sur les fonctions avec les 3e pour l'année 2017-2018 ################################################################ :date: 2018-05-29 -:modified: 2018-05-29 +:modified: 2018-06-04 :tags: Fonctions :category: 3e :authors: Bertrand Benjamin @@ -15,17 +15,32 @@ On demande aux élèves de tracer les graphiques à partir d'un tableau de valeu `Tableau vers graphiques <./E1_tbl_val_graph.pdf>`_ -Étape 2: TICE tracer des graphiques à partir de formules -======================================================== +Étape 2: Découverte de la notion de fonction +============================================ -Au tableau 3 fonctions sous forme de formules, les élèves doivent avec l'outil qu'ils souhaitent tracer le graphique de ces trois fonctions. +(cette étape sert aussi de révision au DNB car les élèves vont être amené à reparcourir leur cahier de bord) -Cahier de bord: Définition d'image et d'antécédent sur la formule, le tableau et le graphique. +Travail individuel, les élèves font une liste des objets mathématiques qu'ils connaissent. On attend à ce qu'ils parlent des nombres (éventuellement avec plus de précision) et des 'formes' géométriques. Certain parleront des équations, ou des lettres. Comme on a déjà vu les fonctions, avec un peu de chance d'autres en viendront à parler des fonctions. -Étape 3: Image et antécédent +On cherche ensuite en groupe à donner une définition à tous les objets découverts. Question pas très facile... On pourra les aider en leur demandant de décrire à quoi servent des objets. Ces définitions/descriptions sont notées dans le cahier de bord. + +On en vient à parler des fonctions pour donner la définition suivante: Une fonction est un objet mathématique qui décrit les transformations des objets mathématiques en d'autres objets mathématiques. + +Individuellement, les élèves cherchent en s'aidant de leur cahier de bord toutes les fonctions que l'on a pu rencontrer sans les nommer. + +Sur le cahier de bord on écrit le liste des fonctions trouvées en insistant sur les objets mathématiques transformés. C'est alors l'occasion de parler de l'image et de l'antécédant. + +Étape 3: Les fonctions numériques +================================= + +Dans le cahier de bord, on donne un exemple de `fonctionsous 3 formes différentes <./E3_fonctions_numeriques.pdf>`_ : formule, tableau de valeur et graphique. Les élèves doivent identifier où se trouve l'image et l'antécédent de chacun de ces exemples. + +Étape 4: Image et antécédent ============================ -3 fonctions données dans 3formes différentes. On pose des questions sur les images et les antécédents. +Au tableau, on écrit des phrases demandant l'image puis l'antécédent de nombres pour différentes fonctions. Une travail individuel puis en groupe, on écrit des phrases faisant intervenir ces notions. + +Les phrases sont réutiliser pour le bilan. Étape 4: Lien entre graphique et formule fonctions linéaire et affine =====================================================================