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\usepackage{myXsim} +\usepackage{tikz} +\usepackage{pgfplots} + \author{Benjamin Bertrand} \title{Fonctions et graphiques - Cours} \date{Septembre 2021} @@ -35,7 +38,36 @@ Déterminer les liens entre les grandeurs est un enjeux important des sciences e Une fonction modélisera \textbf{la transformation} d'une grandeur en une autre. Cela impose des contraintes. -\todo{Ajouter le graphique de la hauteur en fonction de la distance et le graphique de la distance en fonction de la hauteur et ajouter un paragraphe pour expliquer ce qui est modélisable par une fonction et ce qui ne l'est pas.} +\paragraph{Exemple} On reprend l'exemple du lancé de la balle. + +\begin{tikzpicture}[baseline=(current bounding box.south), xscale=1, yscale=1] + \begin{axis}[ticks=none, + domain = 0:5, + ymin=0, + ymax=5, + axis x line=bottom, + axis y line=left, + xlabel={Distance}, + ylabel={Hauteur}] + \end{axis} + \draw[blue] (0,0) plot[domain=1:4, very thick] (\x,{-1.33*\x*\x+6.66*\x-4.33}); +\end{tikzpicture} +\begin{tikzpicture}[baseline=(current bounding box.south), xscale=1, yscale=1] + \begin{axis}[ticks=none, + domain = 0:5, + ymin=0, + ymax=5, + axis x line=bottom, + axis y line=left, + xlabel={Hauteur}, + ylabel={Distance}] + \end{axis} + \draw[blue] (0,0) plot[domain=1:4, very thick] ({-1.33*\x*\x+6.66*\x-4.33}, \x); +\end{tikzpicture} + +Le premier graphique montre que l'on peut transformer la distance en une hauteur. On dit que l'on peut exprimer la hauteur en fonction de la distance. + +Par contre, le deuxième montre que l'on ne peut pas transformer la hauteur en la distance car à une hauteur peuvent correspondre deux distances. \end{document}