%
% tikztemplate.tex -- template for standalon tikz images
%
% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
%
\documentclass[tikz]{standalone}
\usepackage{amsmath}
\usepackage{times}
\usepackage{txfonts}
\usepackage{pgfplots}
\usepackage{csvsimple}
\usetikzlibrary{arrows,intersections,math}
\begin{document}
\def\skala{4}
\definecolor{darkgreen}{rgb}{0,0.6,0}
\begin{tikzpicture}[>=latex,thick,scale=\skala]
\def\n{8}

\fill[color=gray!20] (-1.1,-1.1) rectangle (2.1,2.1);
\fill[color=white] (-1.11,-1.11) rectangle (0,0);
\fill[color=white] (0,0) rectangle (1,1);
\fill[color=white] (1,1) rectangle (2.22,2.22);

\draw[->] (-1.1,0) -- (2.3,0) coordinate[label={$x$}];
\draw[->] (0,-1.1) -- (0,2.3) coordinate[label={left:$y$}];

\draw[color=gray!50,line width=1pt] (-1.1,-1.1) -- (2.2,2.2);

\begin{scope}
\clip (-1.1,-1.1) rectangle (2.1,2.1);

\draw[color=red!40,line width=1.4pt]
	plot[domain=0:2.2,samples=100] ({\x},{\x*\x});
\draw[color=red,line width=1.4pt]
	plot[domain=0:2.2,samples=100] ({\x*\x},{\x});

\draw[color=blue!40,line width=1.4pt]
	plot[domain=-1.1:2.2,samples=100] ({\x},{\x*\x*\x});
\draw[color=blue,line width=1.4pt]
	plot[domain=-1.1:2.2,samples=100] ({\x*\x*\x},{\x});

\draw[color=darkgreen!40,line width=1.4pt]
	(0,0)
	--
	plot[domain=-3:0.1,samples=100] ({exp(\x)},{exp(2*\n*\x)});
\draw[color=darkgreen,line width=1.4pt]
	(0,0)
	--
	plot[domain=-3:0.1,samples=100] ({exp(2*\n*\x)},{exp(\x)});

\draw[color=orange!40,line width=1.4pt]
	plot[domain=0.02:-2,samples=100] ({-exp(\x)},{-exp((2*\n+11)*\x)})
	--
	(0,0)
	--
	plot[domain=-2:0.05,samples=100] ({exp(\x)},{exp((2*\n+11)*\x)});
\draw[color=orange,line width=1.4pt]
	plot[domain=0.02:-2,samples=100] ({-exp((2*\n+11)*\x)},{-exp(\x)})
	--
	(0,0)
	--
	plot[domain=-2:0.05,samples=100] ({exp((2*\n+11)*\x)},{exp(\x)});

\end{scope}

\draw (-1,{0.1/\skala}) -- (-1,{-0.1/\skala});
\node at (-1,{0.1/\skala}) [above] {$-1$};
\draw (1,{0.1/\skala}) -- (1,{-0.1/\skala});
\node at (1,{-0.1/\skala}) [below] {$1$};
\draw (2,{0.1/\skala}) -- (2,{-0.1/\skala});
\node at (2,{-0.1/\skala}) [below] {$2$};

\draw ({-0.1/\skala},-1) -- ({0.1/\skala},-1);
\node at ({0.1/\skala},-1) [right] {$-1$};
\draw ({-0.1/\skala},1) -- ({0.1/\skala},1);
\node at ({-0.1/\skala},1) [left] {$1$};
\draw ({-0.1/\skala},2) -- ({0.1/\skala},2);
\node at ({-0.1/\skala},2) [left] {$2$};

\node at (0,0) [below right] {$0$};

\node[color=orange] at (1.05,2.1) [above left] {$x^{27}$};
\node[color=darkgreen] at (1.03,2.1) [above right] {$x^{16}$};
\node[color=blue] at (1.30,2.1) [above] {$x^3$};
\node[color=red] at ({sqrt(2.1)-0.04},2.1) [above right] {$x^2$};

\node[color=orange] at (2.05,1.04) [below right]
	{$\root{27}\of{x\mathstrut}$};
\node[color=darkgreen] at (2.05,1.03) [above right]
	{$\root{16}\of{x\mathstrut}$};
\node[color=blue] at (2.07,1.28) [right]
	{$\root{3}\of{x\mathstrut}$};
\node[color=red] at (2.05,{sqrt(2.05)-0.02}) [above right]
	{$\sqrt{x\mathstrut}$};

\end{tikzpicture}
\end{document}