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我怎样才能自动绘制此图中的红色虚线？

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我怎样才能自动绘制此图中的红色虚线？

我想画这幅画

enter image description here

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
\usepackage{fouriernc}
\begin{document}
\begin{tikzpicture}
\begin{axis}
    [
    declare function={Y(\x)=-\x^3 +3 * \x^2 -4;},
axis line style = very thick,   
    axis lines = center,
    xlabel=$x$,ylabel=$y$,
        domain=-3.5:3.5,
        ymin=-4.5,
        ymax=1,
        xmin=-1.2,
        xmax=3.2,
    samples=100,xtick distance=1,
ytick distance=2,unit vector ratio*=1 1 1,
    width=11cm,
    grid=major,
    grid style={gray!30}
    ]
       \addplot [black, thick] {Y(x)};
       \addplot [black, mark=*,only marks,samples at={0,-1,1,-2,2,3}] {Y(x)};
       \node at (axis cs:-0.25, -0.25) {$O$} ;
\pgfplotsinvokeforeach{1,3}{
       \draw [blue,dashed](axis cs:#1,{Y(#1)}) -- (axis cs:#1,0);
       }
\addplot[color=red,dashed,thick] coordinates {
            (0 ,-2)
            (1, -2)              };

            \addplot[color=red,dashed,thick] coordinates {
            (0 ,-4)
            (3, -4)              };
         \end{axis}
\end{tikzpicture}
\end{document}

我用手试了一下。

答案1

只需使用与蓝线相同的技术，添加

\draw [red,dashed](axis cs:#1,{Y(#1)}) -- (axis cs:0,{Y(#1)});

在循环。

\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
\usepackage{fouriernc}
\begin{document}
\begin{tikzpicture}
\begin{axis}
    [
    declare function={Y(\x)=-\x^3 +3 * \x^2 -4;},
axis line style = very thick,   
    axis lines = center,
    xlabel=$x$,ylabel=$y$,
        domain=-3.5:3.5,
        ymin=-4.5,
        ymax=1,
        xmin=-1.2,
        xmax=3.2,
    samples=100,xtick distance=1,
ytick distance=2,unit vector ratio*=1 1 1,
    width=11cm,
    grid=major,
    grid style={gray!30}
    ]
       \addplot [black, thick] {Y(x)};
       \addplot [black, mark=*,only marks,samples at={0,-1,1,-2,2,3}] {Y(x)};
       \node at (axis cs:-0.25, -0.25) {$O$} ;
\pgfplotsinvokeforeach{1,3}{
       \draw [blue,dashed](axis cs:#1,{Y(#1)}) -- (axis cs:#1,0);
       \draw [red,dashed](axis cs:#1,{Y(#1)}) -- (axis cs:0,{Y(#1)});
       }
\end{axis}
\end{tikzpicture}
\end{document}

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