使用 tikz 绘制多项式函数

Question

我正在尝试绘制此函数：f(x)=(x^2+3x+9)/(3x)。出现错误，提示无法将 9 除以 0，请问有什么解决办法吗？

这是我的代码：

\begin{tikzpicture}
            \draw[step=0.5cm,cyan,very thin] (-1,-1) grid (5,6);
            \draw[black, ->] (-1,0) -- (5,0); 
            \draw[black, ->] (0,-1) -- (0,6);
            \draw[thick, black, ->] (0,0) -- (0.5,0); 
            \draw[thick, black, ->] (0,0) -- (0,0.5);
            \draw [scale=0.5, domain=0:10,samples=25, teal] plot (\x,{(9+(\x)^2+3*\x)/(3*\x)}) ;
            \draw [scale=0.5, domain=-2:10, smooth, variable=\x, blue] plot ({\x}, {-2/3*\x+5}); 
            \filldraw[blue] (3,0.5) node[anchor=south] {$d$};
            \filldraw[teal] (4,2) node[anchor=south] {$\mathcal{C}$};
            \filldraw[black] (3,1.75) node[anchor=south west] {A};
            \filldraw[black] (3,1.75) node[] {$\times$};
            \filldraw[black] (0,0.25) node[anchor=east] {$\overrightarrow{i}$};
            \filldraw[black] (0.25,0) node[ anchor=north] {$\overrightarrow{j}$};
            \filldraw[black] (5,0) node[ anchor=south east] {$x$};
            \filldraw[black] (0,6) node[ anchor=north west] {$y$};
            \foreach \x in {-1,2,3,4,5,6,7,8,9}
            \draw ({\x cm/2},2pt) -- ({\x cm/2},-2pt) node[anchor=north] {$\x$};
            \foreach \y in {2,3,4,5,6,7,8,9,10,11}
            \draw (2pt, {\y cm/2}) -- (-2pt, {\y cm/2}) node[anchor=east]{$\y$};
\end{tikzpicture}

这是错误：

软件包 PGF 数学错误：您要求我用“ 9.0' by0.0”除以“0.0”，但我无法用“{(9+(0)^2+30)/(30）}'）。... 青色] 图 (\x,{(9+(\x)^2+3*\x)/(3*\x)})

编辑 我想要绘制的图形：

Answer 1

绿色多项式函数的域错误。如果将 x 值设置为 0，y 值将为无穷大。对于 x=0.2，y 值为 16.067。这大于 y 轴上的 11。因此，将域设置为 0.2:10。然后绿线的绘图将超出 y 轴的限制，并且看起来与添加的图片相同。

Answer 2

为了解决这个问题，人们使用pgfplots，用它可以轻松生成所示的图片（针对域 0 到 9）。

但是，当绘制定义间隙时（以丑陋的连接线的形式），问题也会再次出现。因此，通常您必须分段绘制函数（就像您必须使用“TikZ-only”一样）。

\documentclass[border=5pt, varwidth]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}[>=latex]
\begin{axis}[%axis equal,
axis lines=middle, 
xmin=-0.0, xmax=9.5,
ymin=-0.5, ymax=11.75,
xtick={1,...,9},
ytick={1,...,11},
grid=major,
samples=222,
xlabel={$x$},
xlabel style = {anchor=south east},
ylabel={$y$},
ylabel style = {anchor=east},
enlarge x limits={abs=0.5},
]
\addplot[draw=green!55!black, thick, mark=none, 
domain=0:9]{(x^2+3*x+9)/(3*x)};    
\end{axis}
\end{tikzpicture}



\begin{tikzpicture}[>=latex]
\begin{axis}[x=5mm, y=5mm,
axis lines=middle, 
xmin=-9.5, xmax=9.5,
ymin=-11.75, ymax=11.75,
xtick={-9,...,9},
ytick={-11,...,11},
grid=major,
samples=222,
xlabel={$x$},
xlabel style = {anchor=south east},
ylabel={$y$},
ylabel style = {anchor=east},
]
\addplot[draw=green!55!black, thick, mark=none, 
domain=0.0:9]{(x^2+3*x+9)/(3*x)};    
\addplot[draw=green!55!black, thick, mark=none, 
domain=-9:-0.1]{(x^2+3*x+9)/(3*x)};    
\end{axis}
\end{tikzpicture}
\end{document}