[Tex/LaTex] How to plot power functions

tikz-pgf

I want to plot y = x^n for n = 1,2,3,4,5 such that x in [0,1] and y in [0,1].

something like this image:

When I want to set xmin and xmax to restrict the domain, the error appear!
Where is wrong!

\documentclass{standalone}
‎\usepackage{tikz}‎
‎\usepackage[customcolors]{hf-tikz}‎‎‎
‎\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}‎[xmin = ‎0, ymin = 0, xmax = 1‎, ymax = 1‎]‎‎
\addplot[color=red,‎smooth‎] {x‎‎};‎‎
\addplot[color=red,‎smooth‎] {x^‎2‎};‎
\addplot[color=red,‎smoo‎th‎] {x^‎3‎};‎‎
\addplot[color=red,‎smooth‎] {x^‎4‎};‎
\end{axis}
\end{‎tikzpicture}‎
\end{document}

Best Answer

An alternative that uses \pgfplotsinvokeforeach to repeat the \addplot:

\documentclass[tikz,margin=2mm]{standalone}
\usepackage{pgfplots}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}[domain=0:1,xmin=0,xmax=1,ymin=0,ymax=1]
            \pgfplotsinvokeforeach{1,2,...,15}{
                \addplot[red,smooth] {x^#1};
            }
        \end{axis}
    \end{tikzpicture}
\end{document}

And a bit more looking like your desired plot:

With:

\documentclass[tikz,margin=2mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            domain=0:1,
            axis equal,
            width=8cm,height=8cm,
            xmin=-0.05,xmax=1.05,
            ymin=-0.05,ymax=1.05,
            axis y line=middle,
            axis x line=middle,
            xtick=\empty,
            ytick=\empty,
        ]
            \pgfplotsinvokeforeach{1,...,20}{
                \addplot[red,smooth] {x^#1};
            }
            \draw[dashed] (1,0) -- (1,1);
            \draw[dashed] (0,1) -- (1,1);
        \end{axis}
    \end{tikzpicture}
\end{document}

And finally, an animation just for fun:

With:

\documentclass[tikz,margin=2mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}
    \foreach \numPowers in {1,...,20}{
        \begin{tikzpicture}
            \begin{axis}[
                domain=0:1,
                axis equal,
                width=8cm,height=8cm,
                xmin=-0.05,xmax=1.05,
                ymin=-0.05,ymax=1.05,
                axis y line=middle,
                axis x line=middle,
                xtick=\empty,
                ytick=\empty,
            ]
                \pgfplotsinvokeforeach{1,...,\numPowers}{
                    \addplot[red,smooth] {x^##1};
                }
                \draw[dashed] (1,0) -- (1,1);
                \draw[dashed] (0,1) -- (1,1);
            \end{axis}
        \end{tikzpicture}
    }
\end{document}

If anyone could comment on why I need ##1 instead of #1 in the \pgfplotsinvokeforeach when its enclosed in an ordinary \foreach, I would be very grateful.

Related Solutions

[Tex/LaTex] How to create new commands in TikZ

Here is a solution via pgfkeys.

First, I create the new family mygrid, I define some keys with their initial values in this family and I define the new command \mygridset to use this family:

\pgfkeys{
  mygrid/.is family,
  mygrid,
  min x/.initial=-5,
  max x/.initial=5,
  min y/.initial=-5,
  max y/.initial=5,
  small step/.initial=.1,
  step/.initial=1,
  big step/.initial=5,
  color/.initial=red,
}
\newcommand\mygridset[1]{\pgfkeys{mygrid,#1}}

Then I define the new command \mygrid with an empty optional parameter. The first lines of this command (the call to \mygridset) changes the values of the keys via #1 then store the value of each key in a macro. The last lines draw the grid with these values.

\newcommand\mygrid[1][]{
  \mygridset{#1,
    min x/.get=\gridminx,
    max x/.get=\gridmaxx,
    min y/.get=\gridminy,
    max y/.get=\gridmaxy,
    small step/.get=\gridsmallstep,
    step/.get=\gridstep,
    big step/.get=\gridbigstep,
    color/.get=\gridcolor
  }

  \draw [step=\gridsmallstep, help lines,\gridcolor!20]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \draw [step=\gridstep, help lines,\gridcolor!40]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \draw [step=\gridbigstep, help lines,\gridcolor!100]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \foreach \x in {\gridminx,...,\gridmaxx} {
    \node[below,font=\tiny] at (\x,\gridminy) {$\x$};
    \node[above,font=\tiny] at (\x,\gridmaxy) {$\x$};
  };
  \foreach \y in {\gridminy,...,\gridmaxy} {
    \node[left,font=\tiny] at (\gridminx,\y) {$\y$};
    \node[right,font=\tiny] at (\gridmaxx,\y) {$\y$};
  };
}

Here is a complete example (3 pages) to illustrate the usage:

enter image description here

And the complete code:

\documentclass[tikz]{standalone}

\pgfkeys{
  mygrid/.is family,
  mygrid,
  min x/.initial=-5,
  max x/.initial=5,
  min y/.initial=-5,
  max y/.initial=5,
  small step/.initial=.1,
  step/.initial=1,
  big step/.initial=5,
  color/.initial=red,
}
\newcommand\mygridset[1]{\pgfkeys{mygrid,#1}}
\newcommand\mygrid[1][]{
  \mygridset{#1,
    min x/.get=\gridminx,
    max x/.get=\gridmaxx,
    min y/.get=\gridminy,
    max y/.get=\gridmaxy,
    small step/.get=\gridsmallstep,
    step/.get=\gridstep,
    big step/.get=\gridbigstep,
    color/.get=\gridcolor
  }

  \draw [step=\gridsmallstep, help lines,\gridcolor!20]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \draw [step=\gridstep, help lines,\gridcolor!40]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \draw [step=\gridbigstep, help lines,\gridcolor!100]
  (\gridminx,\gridminy) grid (\gridmaxx,\gridmaxy);
  \foreach \x in {\gridminx,...,\gridmaxx} {
    \node[below,font=\tiny] at (\x,\gridminy) {$\x$};
    \node[above,font=\tiny] at (\x,\gridmaxy) {$\x$};
  };
  \foreach \y in {\gridminy,...,\gridmaxy} {
    \node[left,font=\tiny] at (\gridminx,\y) {$\y$};
    \node[right,font=\tiny] at (\gridmaxx,\y) {$\y$};
  };
}

% a style to memorize some change to the default values
\mygridset{
  a grid/.style={
    min x=-3,
    max x=3,
    min y=-3,
    max y=3,
    small step=.2,
    step=1,
    big step=2,
    color=orange,
  }
}

\begin{document}
\begin{tikzpicture}
  % a grid with default values
  \mygrid
\end{tikzpicture}
\begin{tikzpicture}
  % a grid with specific values 
  \mygrid[min x=-3, max x=2,min y=-2,max y=1,color=blue]
\end{tikzpicture}
\begin{tikzpicture}
  % a grid using the `a grid` style
  \mygrid[a grid]
\end{tikzpicture}
\end{document}

[Tex/LaTex] Automatically get (ymin,ymax) and (xmin,xmax) in pgfplots

To prevent PGFPlots from adding padding around your data, set enlargelimits=false:

\documentclass[]{article}

\usepackage{pgfplots}

\begin{document}
Default settings:

\begin{tikzpicture}
\begin{axis}
\addplot table {
3 2
5 3
9 11
};
\end{axis}
\end{tikzpicture}

\hspace{2cm}


With \verb|enlargelimits=false|:

\begin{tikzpicture}
\begin{axis}[enlargelimits=false]
\addplot table {
3 2
5 3
9 11
};
\end{axis}
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] How to create new commands in TikZ

[Tex/LaTex] Automatically get (ymin,ymax) and (xmin,xmax) in pgfplots

Related Question