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使用 TikZ 对该函数进行正确的绘图

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使用 TikZ 对该函数进行正确的绘图

我又来求助了。我需要用 TikZ 绘制函数 $\frac{1}{x+2}$，突出显示 $x = -2$ 处的垂直渐近线。

我想用黑色虚线画出垂直渐近线，用红色画出函数。我想让函数的所有端点都用虚线画出。我设法写了一个代码，但说实话：它很糟糕。

而且我画的渐近线甚至没有经过 $-2$......

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\begin{document}
\begin{tikzpicture}

\begin{scope}[shift={(-10,0)}]
% x & y axis plus scale
\foreach \x in { -3, -2, -1, 1, 2, 3, 4}{
    \draw (\x,.1)--(\x,-.1) node[below,fill=white]() {\footnotesize $\x$};
}
\foreach \y in {-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5}{
    \draw (.1,\y)--(-.1,\y) node[left,fill=white]() {\footnotesize $\y$};
}
\draw[->,line width=.5pt, very thick, -{Stealth}] (-5.5,0)-- (5,0) node[right]()     {$\mathbf{x}$};
\draw[->,line width=.5pt, very thick, -{Stealth}] (0,-5.5)-- (0,5.3) node[above]()     {$\mathbf{y}$};

\node at (2, 2.2) () {$f(x) = \frac{1}{x-2}$};
\node at(.2,-.2) () {\footnotesize $0$};

% Function plot
\begin{scope}
    \clip (-1.99,-4) rectangle (4,4);
    \draw[red, smooth, domain=-3.6:3.6, line width=1pt] plot (\x, {1/(\x+2)});
\end{scope}

% Clipping for dashed line
\begin{scope}
    \clip (0.1,-4.6) rectangle (4,4.5);
    % Dashed vertical line at x = -2
    \draw[dashed, black, line width=1pt] (-2,-4) -- (-2,4);
\end{scope}
\end{scope}

\end{tikzpicture}
\end{document}

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答案1

解决方案如下tikz：

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代码（根据@Henry代码修改）：

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}

\begin{document}
    \begin{tikzpicture}
            % x & y axis plus scale
            \foreach \x in { -4,-3, -2, -1, 1, 2, 3, 4}{
                \draw (\x,.1)--(\x,-.1) node[below,fill=white]() {\footnotesize $\x$};
            }
            \foreach \y in { -4, -3, -2, -1, 1, 2, 3, 4}{
                \draw (.1,\y)--(-.1,\y) node[left,fill=white]() {\footnotesize $\y$};
            }
            \draw[->,line width=.5pt, very thick, -{Stealth}] (-4,0)-- (4.2,0) node[right]()     {$\mathbf{x}$};
            \draw[->,line width=.5pt, very thick, -{Stealth}] (0,-4)-- (0,4.2) node[above]()     {$\mathbf{y}$};
            
            \node at (2, 2.2) () {$f(x) = \frac{1}{x-2}$};
            \node at(.2,-.2) () {\footnotesize $0$};
            \clip (-4,-4) rectangle (4,4);
            \draw[red, smooth, domain=-4:4, line width=1pt,samples=51] plot (\x, {1/(\x+2)});
            \draw[white,line width=3pt,opacity=1] (-2,-5) -- (-2,5);% <<< to cover the red line!    
        
                % Dashed vertical line at x = -2
            \draw[dashed, black, line width=2pt] (-2,-5) -- (-2,5);
    \end{tikzpicture}
\end{document}

答案2

像这样：

在此处输入图片描述

代码：

\documentclass[margin=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            axis lines=middle,
            axis on top,                       
            xmin=-4,   xmax=4,
            ymin=-5,    ymax=5,   
            no markers,                 
            restrict y to domain=-10:10, 
            %
            xlabel=$x$,
            ylabel=$f(x)$           
            ]
            \addplot +[thick,samples=101,smooth]{1/(x+2};         
            \draw[dashed,line width=1pt] (-2,-5)--(-2,5);
        
        \end{axis}
    \end{tikzpicture}
\end{document}

添加：pgfplots将域向左扩展没有问题。

在此处输入图片描述

修改后的主体代码：

\begin{tikzpicture}
    \begin{axis}[
        axis lines=middle,                     
        xmin=-7.5,   xmax=4.5,
        ymin=-5,    ymax=5,   
        no markers,                 
        restrict y to domain=-10:10, 
        %
        xlabel=$x$,
        ylabel=$y$          
        ]
        \addplot +[domain=-7:4,thick,samples=101,smooth]{1/(x+2};         
        \draw[dashed,line width=1pt] (-2,-5)--(-2,5);
        \node[blue,fill=cyan!30] at (2,3) () {$y=\frac{1}{x+2}$};
        \draw[fill=black] (0,.5) circle(.05) node[right,inner sep=1pt](a) {};
        \draw[latex-](a)--(1,1) node[right] {\tiny $A\left(0,\frac12\right) $};
    \end{axis}
\end{tikzpicture}

答案3

  • 我认为绘制图表的正确方法在第二个示例中给出，该示例与我们pgfplots在第二个答案中的包相同
  • 这里有一些小的变化，仅用于练习（代码中的差异已标记）：
%\documentclass[12pt]{article}
\documentclass[12pt, margin=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}

\begin{document}
    \begin{tikzpicture}[
    dot/.style = {circle, fill, semitransparent, inner sep=2pt},
    every pin/.append style = {pin edge={<-,black}, font=\footnotesize, anchor=west,
                                inner sep=1pt}
                        ]
\begin{axis}[axis lines=middle,
             axis on top,
             enlargelimits=0.08,        % <---
             %
             xlabel=$x$,
             ylabel=$y$,
             %
             ymin=-6,   ymax=6,         % <--- changed
             restrict y to domain=-10:10,
             %
             ticklabel style = {rounded corners,
                                font=\tiny, fill=white, inner sep=1pt},   % <---
            xtick = {-6, -5, ..., -1},                                               % <---
            xticklabel style = {anchor=south, yshift=4pt},                      % <---
            extra x ticks={0,1,...,4},                                              % <---
            extra x tick style={xticklabel style={anchor=north,yshift=-4pt}},   % <---
             %
             domain=-6.5:4.5,       % <--- changed
             samples=201,           % <--- changed
             no markers,
            ]
\addplot +[thick]   {1/(x+2)};
\draw[densely dashed, very thin] 
    (-2,\pgfkeysvalueof{/pgfplots/ymin}) -- 
    (-2,\pgfkeysvalueof{/pgfplots/ymax});                                       % <--- changed
\node[dot, pin=above right:{$\bigl(0,\frac{1}{2}\bigr)$}] at (0,{1/(0+2)}) {};  % <--- changed
\node[fill=blue!30, right, font=\footnotesize] at (1,4) {$y=\frac{1}{x+2}$};
\end{axis}
    \end{tikzpicture}
\end{document}

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