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繪製和標記漸近線

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繪製和標記漸近線

如何標示有理函數 y=(x+1)/(x-1) 的漸近線？我\draw[dashed,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}})從另一個帖子複製了代碼。我在手冊中查找了此編碼。我從手冊中得到的唯一“東西”是“軸描述cs”是“坐標系（cs）”的一些描述，而{1,1}指的是某個盒子的右上角。我認為“|-”指示 TikZ 畫一條垂直線。

我不知道如何修改程式碼讓 TikZ 繪製水平漸近線 y=1。如何將標籤“x=1”放在底部箭頭處，將“y=1”放在左側箭頭處？

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

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsthm}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-3}
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=250,domain=-15:15] {(x+2)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}});
\draw [fill=white] (-3,0.25) circle [radius=1.5pt] node[left]{};
\end{axis}
\end{tikzpicture}
\vskip0.25in


\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-1},ytick=\empty
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=251,domain=-14:16] {(x+1)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}});
\end{axis}
\end{tikzpicture}

\end{document}

答案1

您可以使用 anode來放置x=1and y=1。此外，要在 處繪製水平線y=1，您可以使用\addplot：像

\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};

完整程式碼：

\documentclass[10pt]{amsart}
%\usepackage{tikz}      %% These are all not needed
%\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
%\usepackage{tkz-euclide}
%\usetkzobj{all}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

%\usepackage{amsmath}
%\usepackage{amsfonts}
%\usepackage{amssymb}
%\usepackage{amsthm}

\begin{document}

\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-3},
    every axis y label/.style=
         {at={(ticklabel cs:1.02,-12pt)},rotate=0,anchor=west},
    every axis x label/.style={
         at={(xticklabel cs:1.02,-8pt)},anchor=south},
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=250,domain=-15:15] {(x+2)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}})node[right,pos=0.95]{$x=1$};
\draw [fill=white] (-3,0.25) circle [radius=1.5pt] node[left]{};
\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};
\end{axis}
\end{tikzpicture}
\vskip0.25in


\begin{tikzpicture}
\begin{axis}[width=4in,axis equal image,
    axis lines=middle,
    xmin=-15,xmax=15,
    xlabel=$x$,ylabel=$y$,
    ymin=-10,ymax=10,
    restrict y to domain=-12:12,
    enlargelimits={abs=1cm},
    axis line style={latex-latex},
    ticklabel style={font=\tiny,fill=white},
    xtick={-1},ytick=\empty,
    every axis y label/.style=
         {at={(ticklabel cs:1.02,0pt)},rotate=0,},
    every axis x label/.style={
         at={(xticklabel cs:1.02,-8pt)},anchor=south},
]
/pgfplots/xlabel shift={10pt};
\addplot[samples=251,domain=-14:16] {(x+1)/(x-1)};
\draw[dashed,shorten <=2ex, shorten >=2ex,latex-latex] ({{1,0}}|-{{axis description cs:1,1}}) -- ({{1,0}}|-{{axis description cs:1,0}})node[right,pos=0.95]{$x=1$};
\addplot[samples=200,dashed,latex-latex,domain=-17:17] {1}node[above,pos=0]{$y=1$};

\end{axis}
\end{tikzpicture}

\end{document}

在此輸入影像描述

答案2

此語法指示 TikZ 使用垂直線 through和水平線 through(c1 |- c2)的交點處的座標。換句話說：從 開始，向上或向下（沿 y 方向）移動，直到位於 旁邊。這是您指定的點。c1c2c1c2

類似地，(c1 -| c2)與穿過 的水平線c1和穿過 的垂直線相交c2。

PGF 手冊（不是 PGFplots 手冊）第 13.3 節交點座標對此進行了更詳細的解釋。

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