使用 TikZ 绘制对称函数

Question

我一直在尝试绘制以下由 ln(2x²-1)/(x²-1) 定义的函数，该函数应该产生一个对称图。绘制图形右侧时，我什么也没做，只是沿 y 轴反射域，但结果不是对称图。发生了什么？

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
    \draw[gray!20] (-2.9,-2.9) grid (2.9,2.9);
    \draw[-latex,thick] (-3,0)--(3,0) node[right]{$x$};
    \draw[-latex,thick] (0,-3)--(0,3) node[above]{$y$};     
    \foreach \x in {-2,-1,1,2}
    \draw (\x,.1)--(\x,-.1) node[below] {\x};   
    \foreach \y in {-2,-1,1,2}
    \draw (-.1,\y)--(.1,\y) node[right] {\y};
    \draw[thick,blue!50!black, domain=-3:-1.15,smooth,variable=\x] plot ({\x},{(ln(2\x*\x-1))/(\x*\x-1)});
%%% Something is wrong with the following plot %%%
    \draw[thick,blue!50!black, domain=1.15:3,smooth,variable=\x] plot ({\x},{(ln(2\x*\x-1))/(\x*\x-1)});
\end{tikzpicture}
\end{document}

Answer 1

因此，您只需使用显式乘法来避免数字的“错误”扩展。

\documentclass{article}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
    \draw[gray!20] (-2.9,-2.9) grid (2.9,2.9);
    \draw[-latex,thick] (-3,0)--(3,0) node[right]{$x$};
    \draw[-latex,thick] (0,-3)--(0,3) node[above]{$y$};     
    \foreach \x in {-2,-1,1,2}
    \draw (\x,.1)--(\x,-.1) node[below] {\x};   
    \foreach \y in {-2,-1,1,2}
    \draw (-.1,\y)--(.1,\y) node[right] {\y};
    \draw[thick,blue!50!black, domain=-3:-1.15,smooth,variable=\x] plot ({\x},{(ln(2*\x*\x-1))/(\x*\x-1)});
%%% Something is wrong with the following plot %%%
    \draw[thick,blue!50!black, domain=1.15:3,smooth,variable=\x] plot ({\x},{(ln(2*\x*\x-1))/(\x*\x-1)});
\end{tikzpicture}
\end{document}