Feat: qui est-ce des fonctions
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usepackage{pgfplots}
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\pgfplotsset{compat = newest}
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\usepgfplotslibrary{external}
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\tikzexternalize
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\author{Benjamin Bertrand}
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\title{Fonctions tableaux - Exercices}
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\date{2021-10-18}
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\pagestyle{empty}
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\begin{document}
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\begin{tikzpicture}
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% {0.1*(x+4)*(x+1)*(x-5)}
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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legend entries={$f(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% 1/x
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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legend entries={$g(x)$}
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]
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\addplot[domain=-6:-0.1,samples=40, color=red, very thick]{1/x};
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\addplot[domain=0.1:6,samples=40, color=red, very thick]{1/x};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% -x^2 + 2x + 1
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=10,
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legend pos = north east,
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legend entries={$h(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{-2*x^2 + 2*x + 1};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% 2x + 1
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=5,
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legend pos = north west,
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legend entries={$i(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{2*x +1};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% x^2 - 2x - 3
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=10,
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legend pos = north west,
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legend entries={$j(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% xCos(x)
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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legend entries={$k(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{x*cos(deg(x))};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% x sin(2x)
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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legend entries={$l(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% -0.5x + 4
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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legend entries={$m(x)$}
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{-1.75*x+4};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\clearpage
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\begin{tikzpicture}
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% {0.1*(x+4)*(x+1)*(x-5)}
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% 1/x
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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]
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\addplot[domain=-6:-0.1,samples=40, color=red, very thick]{1/x};
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\addplot[domain=0.1:6,samples=40, color=red, very thick]{1/x};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% -x^2 + 2x + 1
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=10,
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legend pos = north east,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{-2*x^2 + 2*x + 1};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% 2x + 1
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=5,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{2*x +1};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% x^2 - 2x - 3
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=10,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% xCos(x)
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{x*cos(deg(x))};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\begin{tikzpicture}
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% x sin(2x)
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))};
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\end{axis}
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\end{tikzpicture}
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\hspace{2cm}
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\begin{tikzpicture}
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% -0.5x + 4
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\begin{axis}[
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axis lines = center,
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%grid = both,
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xlabel = {$x$},
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xtick distance=1,
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ylabel = {$y$},
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ytick distance=1,
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legend pos = north west,
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]
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\addplot[domain=-6:6,samples=40, color=red, very thick]{-1.75*x+4};
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\end{axis}
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\end{tikzpicture}
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\vfill
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\end{document}
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Binary file not shown.
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@ -0,0 +1,27 @@
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\documentclass[12pt,xcolor=table]{classPres}
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\title{Tableaux pour decrire les fonctions}
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\date{Décembre 2021}
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\begin{document}
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\begin{frame}[fragile]{"Qui est-ce?" des fonctions}
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Objectif: Identifier les caractéristiques des graphiques de fonctions qui permettent de les identifier efficacement.
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\vfill
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En groupe de 3:
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\begin{itemize}
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\item \textbf{Descripteur}: décrire oralement le graphique.
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\item \textbf{Devineur}: doit identifier la fonction décrite.
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\item \textbf{Observateur}: prend des notes sur les éléments qui lui semblent les plus efficace pour identifier le graphique.
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\end{itemize}
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\vfill
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\end{frame}
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\end{document}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "master"
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%%% End:
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@ -2,7 +2,7 @@ Fonctions tableaux
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##################
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:date: 2021-10-18
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:modified: 2021-11-01
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:modified: 2021-12-14
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:authors: Benjamin Bertrand
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:tags: Fonctions
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:category: 2nd
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@ -11,7 +11,16 @@ Fonctions tableaux
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Étape 1: Qui est-ce des fonctions
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=================================
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Les élèves sont en binômes. Ils ont chacun un ensemble de graphiques et ne peuvent voir que le leur. Alternativement, ils vont essayer de faire deviner à l'autre la fonction qu'ils auront choisi. Ils n'auront pas le droit de donner des valeurs de la fonction. Il faudra ensuite qu'ils fassent un bilan sur les éléments de description qui sont les plus efficace pour reconnaitre les fonctions.
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Les élèves sont en trinômes. Ils se répartissent les rôles: descripteur, devineur et observateur.
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Le descripteur a une pile de graphique dans laquelle il va tirer un carte après l'autre. Il va devoir décrire la fonction au devineur. Quand le devineur pense avoir identifié la fonction il donne le nom de la fonction et le desripteur le note sur le graphique.
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Pendant ce temps, l'observateur note les éléments de descriptions qui lui ont semblé pertinents pour identifier la fonction.
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.. image:: ./1E_qui_est_ce_fonctions.pdf
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:height: 200px
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:alt: Fonctions pour le qui est-ce
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On espère que sorte la notion de signe d'une fonction et de variations. Ce qui nous permettra d'introduire la notion de tableau de signes et de variations.
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@ -26,3 +35,8 @@ A partir de graphique et de fonctions (à tracer avec la calculatrice) les élè
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===================================
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On donne des tableaux les élèves doivent dans un premier temps tracer des graphiques qui peuvent correspondre. On pourra ajouter un exercice d'analyse d'un tableau pour trouver des extremums.
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Étape 4: tableau de signe et inéquations
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========================================
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