Cfrgtkky

I want to do a little graphical illustration of fixed points of the cubic function. Hence, I made a GeoGebra file that looks like:

Based on that I would like to get a TikZ picture, so GeoGebra created the following code:

documentclass[10pt]{article}

usepackage{pgf,tikz,pgfplots}

pgfplotsset{compat=1.15}

usepackage{mathrsfs}

usetikzlibrary{arrows}

pagestyle{empty}

begin{document}

definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}

begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=3.393473219840507cm,y=3.1433709561724212cm, scale = 0.9, transform shape]

begin{axis}[

x=3.393473219840507cm,y=3.1433709561724212cm,

axis lines=middle,

xmin=-1.3734914110429448,

xmax=1.62708588957055,

ymin=-1.1911483659319086,

ymax=1.353890101224171,

xtick={-1.0,0.0,1.0},

ytick={-1.0,0.0,1.0},]

clip(-1.5734914110429448,-1.1911483659319086) rectangle (2.162708588957055,3.353890101224171);

draw[line width=0.8pt,smooth,samples=100,domain=-1.5734914110429448:1.962708588957055] plot(x,{(x)^(3.0)});

draw [line width=0.8pt,domain=-1.5734914110429448:1.962708588957055] plot(x,{(-0.--1.*x)/1.});

draw (-1.3945119631901841,-0.6566295470542595) node[anchor=north west] {fixed point at $x = -1$};

draw [->,line width=0.4pt] (-1.1269670132777865,-0.8093097675291255) -- (-1.0267447347382272,-0.9581246659666529);

draw (1.1573010736196316,0.8952972509370971) node[anchor=north west] {fixed point at $x = 1$};

draw (0.162066871165644,-0.20714781299805446) node[anchor=north west] {fixed point at $x = 0$};

draw (1.3389923312883434,1.3508530624805482) node[anchor=north west] {$y = x $};

draw (0.5803595092024538,1.3417419462496791) node[anchor=north west] {$f(x) = x^3$};

draw (0.01834095092024525,1.36300121745504) node[anchor=north west] {$f(x)$};

draw (1.5159338957055212,0.14514868126221436) node[anchor=north west] {$x$};

draw [->,line width=0.4pt] (0.1593550613496931,-0.23144412294703853) -- (0.02376457055214709,-0.027962527124297032);

draw [->,line width=0.4pt] (1.1491656441717788,0.843667592295506) -- (1.0298460122699384,0.9742602582712953);

draw [line width=0.8pt,dash pattern=on 1pt off 1pt] (-1.,-1.)-- (-1.,0.);

draw [line width=0.8pt,dash pattern=on 1pt off 1pt] (1.,1.)-- (1.,0.);

begin{scriptsize}

draw [fill=uuuuuu] (1.,1.) circle (2.0pt);

draw [fill=uuuuuu] (-1.,-1.) circle (2.0pt);

draw [fill=uuuuuu] (0.,0.) circle (2.0pt);

end{scriptsize}

end{axis}

end{tikzpicture}

end{document}

That results in

which looks almost like I want it to look like apart from the texts (fixed point at …).

How can I improve the code in order to position the texts (fixed point at …) like in Figure 1 (including the linebreak after "at")? I tried a few little things but nothing seems to work.

This is a proposal.

documentclass[tikz]{standalone}

usetikzlibrary{calc}

begin{document}

begin{tikzpicture}[>=stealth,scale=3]

draw[->] (0,-1.2)--(0,1.4) node[below right] {$f(x)$};

draw[->] (-1.6,0)--(2,0) node[above left] {$x$};

draw[thick] plot[samples=2,domain=-1.2:1.4] (x,x);

draw[thick] plot[smooth,samples=500,domain=-1.06:1.12] (x,x^3);

fill (-1,-1) circle (.5pt) coordinate (a) (0,0) circle (.5pt) coordinate (b) (1,1) circle (.5pt) coordinate (c);

draw[dashed] (-1,-1)--(-1,0) (1,0)--(1,1);

draw (-1,-.03) node[below] {$-1$}--(-1,.03) (1,-.03) node[below] {$1$}--(1,.03);

draw (-.03,-1) node[left] {$-1$}--(.03,-1) (-.03,1) node[left] {$1$}--(.03,1);

draw (1.1,{1.1^3}) node[left] {$f(x)=x^3$};

draw (1.3,1.3) node[below right] {$y=x$};

draw[<-] ($(a)+(150:.05)$)--++(150:.2) node[above left,align=left] {fixed point\at $x=-1$};

draw[<-] ($(b)+(-30:.05)$)--++(-30:.2) node[below right,align=left] {fixed point\at $x=0$};

draw[<-] ($(c)+(-30:.05)$)--++(-30:.2) node[below right,align=left] {fixed point\at $x=1$};

end{tikzpicture}

end{document}

Some notes:

• 
  draw plot helps us draw plot even without pgfplots.


• Library calc helps us calculate coordinates. Read more here
  


• Nodes can be multi-line, however you need to add alignment option (align=...) and/or text width option. Read more here.