3

I want to graph the function (x^(2/3))*(6-x)^(1/3) that is displayed as the results of Geogebra. What i want to show

But I get an error in tikz and it can only be graphed in its domain [0,6]

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\pgfplotsset{compat=1.11}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{angles}
\usetikzlibrary{quotes}

\begin{document}
\definecolor{qqwuqq}{rgb}{0,0.39215686274509803,0}
\begin{tikzpicture}[scale=0.7]
\draw[help lines] (-1 ,-1) grid (6, 4);
\draw[-Latex,line width=1pt,color=black] (-1, 0) -- (6, 0);
\draw[-Latex,line width=1pt,color=black] (0, -1) -- (0, 4);
\draw[color=black] (4,0) node[above] {$x$};
\draw[color=black] (0,4) node[right] {$y$};
    \foreach \x in {-1,0, ...,6} {
        \draw [thick] (\x, 0) -- ++(0, -.2) ++(0, -.15) node [below, outer sep=0pt, inner sep=0pt] {\small\(\x\)};
    }
 \foreach \y in {-1,0, ...,4} {
        \draw [thick] (0, \y) -- ++(-.2, 0) ++(-.15, 0) node [left, outer sep=0pt, inner sep=0pt] {\small\(\y\)};
    }
\clip(-1,-1) rectangle (6.5,4);
\draw[line width=2pt,color=blue,samples=100,domain=0:6] plot(\x,{((\x)^(2/3))*(6-\x)^(1/3)});
\end{tikzpicture}
\end{document}
2

Perhaps a piecewise definition does help...

\documentclass[margin=3mm]{standalone}
    \usepackage{pgfplots}
    \pgfplotsset{compat=1.17}
    \usepackage{mathrsfs}
    \usetikzlibrary{arrows, arrows.meta}

    \begin{document}
        \begin{tikzpicture}
            \begin{axis}[
                axis lines=middle,
                axis line style={thick,-Stealth},
                grid,
                xlabel=$x$,
                xmin=-6.5, xmax=7,
                xtick={-6,-5,...,7},
                ylabel=$y$,
                ytick={-2,-1,...,6},
                ymin=-2.0, ymax=4,
                no marks, samples=300
                ]
                \addplot +[line width=1.5pt,domain=-6:7] 
                       plot {(\x<=6) * ((abs(\x))^(2/3)*(6-\x)^(1/3))   +
                             (\x>6)  * (-((\x)^(2/3)*(\x-6)^(1/3)))};
            \end{axis}
        \end{tikzpicture}
    \end{document}

enter image description here

| improve this answer | |
4

enter image description here

  • Since you load pgfplots package, I using it for drawing your diagram
  • Roots of negative functions' values are imaginary, therefore you can't draw them in pgfplots diagram. However, you can draw roots of their absolute values. In your case for abs(x)^{...} and abs(6-x)^{...} in your function:
\documentclass[margin=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\usepackage{mathrsfs}
\usetikzlibrary{arrows, arrows.meta}

\begin{document}
    \begin{tikzpicture}
\begin{axis}[
axis lines=middle,
axis line style={thick,-Stealth},
grid,
xlabel=$x$,
xmin=-6.5, xmax=7,
xtick={-6,-5,...,6},
ylabel={$y=|x|^{2/3}|6-x|^{1/3}$},
ylabel style = {fill=white, inner sep=0pt,xshift=1ex,anchor=west},
ytick={-1,-0,...,6},
ymin=-1.5, ymax=7,
ticklabel style={font=\footnotesize},
no marks
            ]
\addplot +[line width=2pt,
           samples at={-6,-5.8,...,5.8,5.81,5.82,...,7}] 
           plot {(abs(x)^(2/3))*abs(6-x)^(1/3)};
\end{axis}
    \end{tikzpicture}
\end{document}
| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.