5

I have specified that the function x(1 - x)^{1/5} should be plotted on the domain [-1.5,2.5]. It is only plotted on the domain [1,2.5].

\documentclass[10pt]{amsart}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}

\noindent \hspace*{\fill}
\begin{tikzpicture}
\begin{axis}[width=6in,axis equal image,unit vector ratio={2 1},clip=false,
    axis lines=middle,
    xmin=-1.5,xmax=2.5,
    domain=-1.5:2.5, samples=201,
    xlabel=$x$,ylabel=$y$,
    ymin=-1,ymax=3,
    restrict y to domain=-1:3,
    %enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={\empty},ytick={\empty},
    extra x ticks={0.83333, 1, 1.6666},
    extra x tick labels={$\frac{5}{6}$, $1$, $\frac{5}{3}$},
    extra y ticks={-2},
    extra y tick labels={$ma+b$},
    yticklabel style={anchor=west},
    yticklabel shift=-4pt,
    ticklabel style={font=\tiny,fill=white},
    xtick={0.83333, 1, 1.6666},ytick={\empty},
    xlabel style={at={(ticklabel* cs:1)},anchor=north west},
    ylabel style={at={(ticklabel* cs:1)},anchor=south west}
]
\addplot[samples=501,domain=-1.5:2,blue] {x*(x - 1)^(0.2)};
\draw [fill] (0.83333,-0.8034) circle [radius=1.5pt];
\draw [fill] (1,0) circle [radius=1.5pt];
\draw [fill] (1.6666,1.53685) circle [radius=1.5pt];
\end{axis}
\end{tikzpicture}
\hspace{\fill}
\vskip0.2in

\end{document}
percusse
  • 157,807
Adelyn
  • 3,373
  • Why do you persistently tag these as TikZ questions? – percusse Oct 28 '14 at 15:07
  • @percusse. I am not sure what you are referring to as "these." This is a TikZ question. – Adelyn Oct 28 '14 at 15:11
  • x^0.2 is complex for x<0. PGFPlots doesn't handle complex numbers. Perhaps you meant to plot x * abs(x-1)^2? – Jake Oct 28 '14 at 15:25
  • 3
    I have retagged your previous questions too, that's what I mean by these. Pgfplots uses Tikz environment but has its own habitat so searching for pgfplots questions don't include tikz tag. [tag:pgfplots] is a separate tag. So we use to tag those. – percusse Oct 28 '14 at 15:44
  • @Jake I guess that x^{0.2} is interpreted as x^{1/5}, which is defined on the set of all real numbers. Anyway, pgfplots is not plotting this function at 1. The function value is 0. – Adelyn Oct 28 '14 at 16:10
  • @percusse I will distinguish between questions on TikZ and questions on pgfplots. – Adelyn Oct 28 '14 at 16:11
  • @Adelyn: PGFPlots is not plotting the function at x=1 because you're not telling it to sample the function there. Your domain runs from -1.5 to 2, and is sampled at 501 evenly spaced locations. The function is therefore evaluated at x=0.999 and at x=1.006. Set samples=301 to get a sample at x=1. I'm not sure what you mean by "interpreted as x^{1/5}, which is defined on the set of all real numbers". Of course the function is defined there, but for negative x the result is a complex number. What do you expect the plot to look like? – Jake Oct 28 '14 at 16:39
  • Rational exponents are calculated using logarithms -- I conjecture that your issue is the same as the one that has been asked previously with cube roots – cmhughes Oct 28 '14 at 17:06
  • @cmhughes: Ah, yes, this one? http://tex.stackexchange.com/questions/19052/pgf-math-function-to-compute-cube-root – Jake Oct 28 '14 at 17:11
  • @jake: not the one I was thinking of, but close enough :) can you use your magic gold-badge powers to close as duplicate? – cmhughes Oct 28 '14 at 18:23
  • @Jake I was thinking either Pgfplots : can't plot some usual mathematical functions or How to plot x^(1/3)? – cmhughes Oct 28 '14 at 21:41
  • @cmhughes: Ah yes. Done! – Jake Oct 28 '14 at 21:46

1 Answers1

5

You can get the real root using 

declare function={
    realroot(\n,\x) = ((abs(\x))^(1/\n))*(\x)/abs(\x);
}

Then you get the following plot, which seems to agree with what WolframAlpha does:

\documentclass[10pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}


\begin{document}
\begin{tikzpicture}[
    declare function={
        realroot(\n,\x) = ((abs(\x))^(1/\n))*(\x)/abs(\x);
    }   
]   
\begin{axis}
\addplot[samples=351,domain=-1.5:2,blue] {
    x*realroot(5,x-1)
};
\end{axis}
\end{tikzpicture}

\end{document}
Jake
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