pgfplots not plotting all of the domain

Question

I am trying to plot the function $-0.5x^{\frac{4}{3}}-x^{\frac{1}{3}}+1.2x+1$ over the interval $[-2,5]$ but the graph for negative $x$ values is not plotting. How do I get the graph when $x$ is negative?

\begin{tikzpicture}
\begin{axis}[
    axis lines = center,
    xlabel = $x$,
    ylabel = $y$,
    xmin = -2.5, xmax = 4.5,
    ymin = -1.5, ymax = 2.5,
    xtick = {-2,-1.191,-0.103,0,0.292,1,2,4.144}]
    \addplot[
        domain = -5:5,
        samples = 200,
        smooth,
        thick,
        blue,
    ] {-0.5x^(4/3)-x^(1/3)+1.2x+1};
\end{axis}
\end{tikzpicture}

score 4 · Accepted Answer · answered Oct 26 '21 at 20:16

This question has been raised before several times (1, 2, 3, 4). The problem seems to lie in the way PGF deals with roots and fractional powers using logarithmic functions. (For more details, see this question.)

As suggested by the author of this answer, you can use the expression x/abs(x)*abs(x)^(1/3) to replace x^(1/3) in order to circumvent the above problem. You would then get:

\documentclass[border=1mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
    axis lines = center,
    xlabel = $x$,
    ylabel = $y$,
    xmin = -2.5, xmax = 4.5,
    ymin = -1.5, ymax = 2.5,
    xtick = {-2,-1.191,-0.103,0,0.292,1,2,4.144},
    x post scale=2]
    \addplot[
        domain = -5:5,
        samples = 200,
        smooth,
        thick,
        blue,
    ] {-0.5x/abs(x)abs(x)^(4/3)-x/abs(x)abs(x)^(1/3)+1.2x+1};
\end{axis}
\end{tikzpicture}
\end{document}

Note that the left half might be wrong here. I get a negative answer when I pass in -1. This worked: \pgfmathdeclarefunction{CubeRoot}{1}{% \pgfmathparse{ifthenelse(#1<0,-1,1)*exp((ln(abs(#1)))/3)}% } — Ungar Linski, Oct 27 '21 at 00:32

score 0 · Answer 2 · answered Oct 26 '21 at 19:45

0

\documentclass[border=1 cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
 \begin{axis}[
    axis lines = center,
    xlabel = $x$,
    ylabel = $y$,
    xmin = -2, xmax = 6,
    ymin = -1.5, ymax = 2.5,
    x tick label style={/pgf/number format/precision=3},
    xtick = {-2,-1.191,-0.103,0,0.292,1,2,4.144},
    x post scale=4,
]
    \addplot[
        domain = -2:6,
        samples = 200,
        smooth,
        thick,
        blue,
    ] {-0.5*x^(4/3)-x^(1/3)+1.2*x+1};
\end{axis}
\end{tikzpicture}
\end{document}

answered Oct 26 '21 at 19:45

hpekristiansen

37,006

Nice! But why is there no graph to the left of the $y$-axis? The function is defined on all real numbers. – Ungar Linski Oct 26 '21 at 19:48
First or all, these are cube roots, not even-powered roots. Second, don't speak to me that way. I explicitly ask for the plot when $x$ is negative as well. – Ungar Linski Oct 26 '21 at 19:52
Asking me for the sqrt(-1) does not add to the question. – Ungar Linski Oct 26 '21 at 19:58

pgfplots not plotting all of the domain

2 Answers2