跳过天花板图中的某些 y 值

Question

我正在尝试ceil(3^x)为域绘制一个0:4图表。我可以很好地得到图表。但是，与x值相比，y范围非常大，并且在y的较高值处跳跃标记几乎很小。所以我想要实现的是保持域原样，即0:4，但对于y值，我们可以从0到5开始，然后从79到81。值得注意的是，跳跃标记是根据x的对数值标记的，我可以手动执行此操作。另外，我想显示y轴的虚线部分，表示已跳过某些y值。我可以通过明确提及它们来省略y刻度标记，例如ytick={0,1,2,3,4,5,79,80,81}，但是，它不会跳过给定范围内所有排除的y值的图表。

\documentclass{standalone}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        set layers,
        axis lines=middle,
        xmin=-0.1,
        xmax=4.5,
        ymin=-2,
        ymax=84.5,
        ytick={0,1,2,3,4,5,79,80,81},
        enlarge y limits=false,
        extra x ticks={0},
        extra y ticks={0},
        xlabel={$x$},
        ylabel={$y$},
            every axis x label/.style={at={(current axis.right of origin)},anchor=north west},
                every axis y label/.style={at={(current axis.above origin)},anchor=east},
        grid,
        grid style=dashed,
        ticklabel style={fill=white,fill opacity=0.7,text opacity=1},
    ]
        \addplot[thick,red,jump mark mid,samples=1000,domain=0:4]{ceil(3^x)};
    \end{axis}
\end{tikzpicture}

\end{document}

更新

感谢 hpekristiansen 的原始回答，这个接近我想要实现的目标。

\documentclass[tikz, border=1cm]{standalone}

\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
\begin{tikzpicture}
\pgfplotsset{
    axis lines=middle,
    xmin=-0.1,
    xmax=4.5,
}
\begin{axis}[
    xlabel={$x$},
    ylabel={$y$},
    ymin=-0.2,
    ymax=10, restrict y to domain=0:5,
    ytick={0,1,2,3,4,5}
]
    \addplot[thick,red,jump mark mid,samples=1000,domain=0:4]{ceil(3^x)};
\end{axis}
\begin{axis}[
    axis x line=none,
    restrict y to domain=78:81,
    ymin=71,
    ymax=82,
    ytick={79,80,81},
]
    \addplot[thick,red,jump mark mid,samples=1000,domain=0:4]{ceil(3^x)};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

\documentclass[tikz, border=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
\pgfplotsset{
axis lines=middle,
xmin=-0.1, xmax=4.5,
y axis line style={draw=none},
}

\begin{axis}[
xlabel={$x$},
ylabel={$y$},
ymin=0, ymax=10, restrict y to domain=0:5,
ytick={0,1,2,3,4,5},
]
\addplot[thick,red,jump mark mid,samples=1000,domain=0:4]{ceil(3^x)};
%manual y-axis
\draw (0,0) -- (0,5.5); \draw[dotted] (0,5.5) -- (0,7); \draw[-stealth] (0,7) -- (0,10);
\end{axis}

\begin{axis}[
axis x line=none,
ymin=71, ymax=82, restrict y to domain=79:81,
ytick={79,80,81},
]
\addplot[thick,red,jump mark mid,samples=1000,domain=0:4]{ceil(3^x)};
\end{axis}

\end{tikzpicture}
\end{document}