我怎样才能通过这张图片得到正确的结果？

Question

我想画成这样

我试过。

第一种方式（我得到了正确的结果）

\documentclass[12pt,border=1mm]{standalone} 
\usepackage{fouriernc} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.16} 
\begin{document} 
\begin{tikzpicture}[>=stealth,declare function={ 
xmin=-1;xmax=10;ymin=-3;ymax=2;}] 
\draw[gray!30] (xmin,ymin) grid (xmax,ymax); % grid 
\draw[->, thick] (xmin,0)--(xmax,0) node [below left]{$x$}; 
\draw[->,thick] (0,ymin)--(0,ymax) node [below left]{$y$}; 
\node[below right] at (0, 0) {$O$}; 
\foreach \p/\g in {1/-90,2/-45,3/-90,4/90,5/-90,6/-45,7/-90,8/-90,9/-90 }\draw(\p,0)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\foreach \p/\g in {-2/180,1/180}\draw(0,\p)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\draw[very thick] (2,0)
arc [start angle=0, end angle=180, radius=1];
\draw[very thick] (6,0)
arc [start angle=0, end angle=-180, radius=2];
\draw[thick] (6,0) -- (9,1);
\foreach \Y in {(2,0),(4,-2),(6,0),(9,1)} \fill \Y circle(2pt); 
\draw[dashed] (9,0) |- (0,1);
\draw[dashed] (4,0) |- (0,-2);
\end{tikzpicture} 
\end{document}

第二种方式（我没有得到正确的结果）

\documentclass[12pt,border=1mm]{standalone} 
\usepackage{fouriernc} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.16}
\begin{document} 
\begin{tikzpicture}[>=stealth,declare function={ 
xmin=-1;xmax=10;ymin=-3;ymax=2;
f(\x)=sqrt(2*\x- \x*\x);
g(\x)=-sqrt(-12 + 8*\x - \x*\x);
}] 
%\draw[gray!30] (xmin,ymin) grid (xmax,ymax); % grid 
\draw[->, thick] (xmin,0)--(xmax,0) node [below left]{$x$}; 
\draw[->,thick] (0,ymin)--(0,ymax) node [below left]{$y$}; 
\node[below right] at (0, 0) {$O$}; 
\foreach \p/\g in {1/-90,2/-45,3/-90,4/90,5/-90,6/-45,7/-90,8/-90,9/-90 }\draw(\p,0)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\foreach \p/\g in {-2/180,1/180}\draw(0,\p)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\draw[thick] (6,0) -- (9,1);
%\foreach \Y in {(2,0),(4,-2),(6,0),(9,1)} \fill \Y circle(2pt); 
\draw[dashed] (9,0) |- (0,1);
\draw[dashed] (4,0) |- (0,-2);
\draw[very thick,blue,smooth,samples=250,domain=0:2] plot(\x,{f(\x)});
\draw[very thick,blue,smooth,samples=250,domain=2:6] plot(\x,{g(\x)});  
\end{tikzpicture} 
\end{document}

我如何通过第二种方式获得正确的结果？

Answer 1

根据这个很棒的答案您需要放置plot function而不是仅添加plot。

我尝试过但找不到在或plot function内使用的方法，因此我删除了它们并用它们的定义替换以获得第一种方法（顺便说一句，我不知道您为什么忘记添加蓝色，黑点和网格背景）：f(\x)g(\x)declare function

\documentclass[12pt,border=1mm]{standalone} 
\usepackage{fouriernc} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.15}
\begin{document} 
\begin{tikzpicture}[>=stealth,declare function={ 
xmin=-1;xmax=10;ymin=-3;ymax=2;
%f(\x)=sqrt(2*\x- \x*\x); % deleted
%g(\x)=-sqrt(-12 + 8*\x - \x*\x); % deleted
}] 
%\draw[gray!30] (xmin,ymin) grid (xmax,ymax); % grid 
\draw[->, thick] (xmin,0)--(xmax,0) node [below left]{$x$}; 
\draw[->,thick] (0,ymin)--(0,ymax) node [below left]{$y$}; 
\node[below right] at (0, 0) {$O$}; 
\foreach \p/\g in {1/-90,2/-45,3/-90,4/90,5/-90,6/-45,7/-90,8/-90,9/-90 }\draw(\p,0)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\foreach \p/\g in {-2/180,1/180}\draw(0,\p)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\draw[thick] (6,0) -- (9,1);
%\foreach \Y in {(2,0),(4,-2),(6,0),(9,1)} \fill \Y circle(2pt); 
\draw[dashed] (9,0) |- (0,1);
\draw[dashed] (4,0) |- (0,-2);
\draw[very thick,blue,smooth,samples=250,domain=0:2] plot function{sqrt(2*x- x*x)};
\draw[very thick,blue,smooth,samples=250,domain=2:6] plot function{-sqrt(-12 + 8*x - x*x)};  
\end{tikzpicture} 
\end{document}

Answer 2

我不知道为什么会发生这种情况（似乎与 cm 和 pt 之间的转换以及一些数值错误有关），manoooh 的答案是更简洁的方法。这只是以防您没有安装 gnuplot。然后您可以“继续”函数，使它们保持明确定义并在稍长的时间间隔内绘图。

\documentclass[12pt,border=1mm]{standalone} 
\usepackage{fouriernc} 
\usepackage{pgfplots} 
\pgfplotsset{compat=1.16}
\begin{document} 
\begin{tikzpicture}[>=stealth,declare function={ 
xmin=-1;xmax=10;ymin=-3;ymax=2;
f(\x)=ifthenelse(2*\x- \x*\x>0,sqrt(abs(2*\x- \x*\x)),0);
g(\x)=-ifthenelse(-12 + 8*\x - \x*\x>0,sqrt(abs(-12 + 8*\x - \x*\x)),0);
}] 
%\draw[gray!30] (xmin,ymin) grid (xmax,ymax); % grid 
\draw[->, thick] (xmin,0)--(xmax,0) node [below left]{$x$}; 
\draw[->,thick] (0,ymin)--(0,ymax) node [below left]{$y$}; 
\node[below right] at (0, 0) {$O$}; 
\foreach \p/\g in {1/-90,2/-45,3/-90,4/90,5/-90,6/-45,7/-90,8/-90,9/-90 }\draw(\p,0)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\foreach \p/\g in {-2/180,1/180}\draw(0,\p)node[shift={(\g:.3)},scale=1]{$\p$}--+(0,.05)--+(0,-.05); 
\draw[thick] (6,0) -- (9,1);
%\foreach \Y in {(2,0),(4,-2),(6,0),(9,1)} \fill \Y circle(2pt); 
\draw[dashed] (9,0) |- (0,1);
\draw[dashed] (4,0) |- (0,-2);
\draw[very thick,blue] plot[smooth,samples=250,domain=0:2.003](\x,{f(\x)});
\draw[very thick,blue] plot[smooth,samples=250,domain=2:6.003](\x,{g(\x)});  
\end{tikzpicture} 
\end{document}