\documentclass{article}
\usepackage[utf8]{inputenc}



\usepackage{pgf,tikz}
\usepackage{pgfplots}
\usetikzlibrary{arrows,backgrounds}
\pgfplotsset{width=10cm,compat=newest}






\title{\#05 Draw graphs of the following functions}
\author{Enrique Andrade González }
\date{Computer tools in mathematican's work}

\begin{document}

\maketitle

\section{$x^2-2x+3$}

\begin{tikzpicture}

    \draw [->] (0,0) -- (0,12);
    \draw [<->] (-4,0) -- (6,0);
    \draw [help lines] (-4,0) grid (6,12);
    % x ^ 2-2x + 3
    \draw [blue, domain=-2:4] plot (\x, {pow(\x,2)-\x*2 +3}) 
    node[right] {$v_1(x^2-2x +3)$)};
    \node [below] at (0,0) {(0,0)};
    \node [above] at (0,12) {(0,12)};
    \node [left] at (-4,0) {(-4,0)};
    \node [right] at (6,0) {(6,0)};

\end{tikzpicture}

\section{cos(2x)}

\begin{tikzpicture}

    \draw [<->] (0,-3) -- (0,3);
    \draw [<->] (-6,0) -- (6,0);
    \draw [help lines] (-6,-3) grid (6,3);
    % x ^ 2-2x + 3
    \draw [blue, domain=-6:6] plot (\x, {cos(\x*2 r)}) 
    node[right] {$v_1(cos(x*2))$};
    \node [below] at (0,0) {(0,0)};
    \node [above] at (0,3) {(0,3)};
    \node [left] at (-6,0) {(-6,0)};
    \node [right] at (6,0) {(6,0)};
    \node [below] at (0,-3) {(0,-3)};

\end{tikzpicture}


\section{sin(1/x)}

\begin{tikzpicture}

    \draw [<->] (0,-3) -- (0,3);
    \draw [<->] (-6,0) -- (6,0);
    \draw [help lines] (-6,-3) grid (6,3);
    %% Problema!!! Vale esta solución???
    \draw [blue, domain=0.01:6, rotate=180] plot (\x, {sin(1/\x r)});
    % Problema al tener un 0 en el denominador.
    \draw [blue, domain=0.01:6] plot (\x, {sin(1/\x r)})
    node[right] {$v_1(x^2-2x +3)$)};
    \node [below] at (0,0) {(0,0)};
    \node [above] at (0,3) {(0,3)};
    \node [left] at (-6,0) {(-6,0)};
    \node [right] at (6,0) {(6,0)};
    \node [below] at (0,-3) {(0,-3)};

\end{tikzpicture}


\section{x^2+y^2}

\begin{tikzpicture}

\begin{axis}[
%hide axis,
xlabel=$x$,ylabel=$y$,mesh/interior colormap name=hot,colormap/blackwhite,]
\addplot3[domain=-3:3,surf,samples=41]
{x^2+y^2};
\end{axis}

\end{tikzpicture}


\section{x^2-y^2+2*x*y^2+1}

\begin{tikzpicture}

\begin{axis}[
%hide axis,
xlabel=$x$,ylabel=$y$,mesh/interior colormap name=hot,colormap/blackwhite,]
\addplot3[domain=-3:3,surf,samples=41]
{x^2-y^2+2*x*y^2+1};
\end{axis}

\end{tikzpicture}

\end{document}