2021-2022/2nd/09_Fonctions_tableaux/1E_qui_est_ce_fonctions.tex

\documentclass[a4paper,10pt]{article}
\usepackage{myXsim}
\usepackage{pgfplots}
\pgfplotsset{compat = newest}
\usepgfplotslibrary{external} 
\tikzexternalize

\author{Benjamin Bertrand}
\title{Fonctions tableaux - Exercices}
\date{2021-10-18}

\pagestyle{empty}


\begin{document}

\begin{tikzpicture}
    % {0.1*(x+4)*(x+1)*(x-5)}
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$f(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 1/x
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$g(x)$}
        ]
        \addplot[domain=-6:-0.1,samples=40, color=red, very thick]{1/x};
        \addplot[domain=0.1:6,samples=40, color=red, very thick]{1/x};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -x^2 + 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north east,
        legend entries={$h(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-2*x^2 + 2*x + 1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=5,
        legend pos = north west,
        legend entries={$i(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x +1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x^2 - 2x - 3
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        legend entries={$j(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % xCos(x)
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$k(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x*cos(deg(x))};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x sin(2x)
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$l(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % -0.5x + 4
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$m(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-1.75*x+4};
    \end{axis}
\end{tikzpicture}
\vfill


\clearpage


\begin{tikzpicture}
    % {0.1*(x+4)*(x+1)*(x-5)}
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 1/x
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        ]
        \addplot[domain=-6:-0.1,samples=40, color=red, very thick]{1/x};
        \addplot[domain=0.1:6,samples=40, color=red, very thick]{1/x};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -x^2 + 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north east,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-2*x^2 + 2*x + 1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=5,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x +1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x^2 - 2x - 3
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % xCos(x)
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x*cos(deg(x))};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x sin(2x)
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % -0.5x + 4
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-1.75*x+4};
    \end{axis}
\end{tikzpicture}
\vfill

\clearpage

\begin{tikzpicture}
    % 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$f(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x+1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 2x - 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        legend pos = north west,
        legend entries={$g(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x - 1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -0.5x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north east,
        legend entries={$h(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-0.5*x+1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % -0.5x - 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=5,
        legend pos = north west,
        legend entries={$i(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-0.5*x - 1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x^2 - 2x - 3
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        legend entries={$j(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % x^2 - 2x 
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        legend entries={$k(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x^2 - 2*x};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -x^2 + 2x
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        legend entries={$l(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-x^2 + 2*x};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % x^2 + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        legend pos = north west,
        legend entries={$m(x)$}
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x^2 + 1};
    \end{axis}
\end{tikzpicture}
\vfill

\clearpage

\begin{tikzpicture}
    % 2x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x+1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % 2x - 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=1,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x - 1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -0.5x + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-0.5*x+1};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % -0.5x - 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=5,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-0.5*x - 1};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % x^2 - 2x - 3
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{2*x^2 - 2*x - 3};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % x^2 - 2x 
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x^2 - 2*x};
    \end{axis}
\end{tikzpicture}
\vfill
\begin{tikzpicture}
    % -x^2 + 2x
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{-x^2 + 2*x};
    \end{axis}
\end{tikzpicture}
\hspace{2cm}
\begin{tikzpicture}
    % x^2 + 1
    \begin{axis}[
        axis lines = center,
        %grid = both,
        xlabel = {$x$},
        xtick distance=1,
        ylabel = {$y$},
        ytick distance=10,
        ]
        \addplot[domain=-6:6,samples=40, color=red, very thick]{x^2 + 1};
    \end{axis}
\end{tikzpicture}
\vfill

\end{document}