如何在 tikz 上绘制自定义函数？

Question

我使用 powerpoint 笔/记号笔工具任意绘制了一个函数，如下例所示。但不知道该如何将其转换为 tikz？我是否必须使用一些已知的函数近似值？任何帮助都非常感谢。

预期：（我用钢笔/记号笔工具在 MS PowerPoint 上画了这幅图）

我的结果：

代码：

\documentclass[border=3pt,tikz]{standalone}
\usepackage{tikz}
\usepackage{etoolbox} % for \ifnumcomp
\usepackage{listofitems} % for \readlist to create arrays

\tikzset{>=latex} % for LaTeX arrow head

\def\nstyle{int(\lay<\Nnodlen?min(2,\lay):3)} % map layer number onto 1, 2, or 3
\usetikzlibrary{positioning, calc, arrows.meta}
\begin{document}

\begin{tikzpicture}

\begin{scope}[scale=0.75,xshift=18cm,yshift=-2cm] % <---- HERE
    \draw[blue!50!black] plot[domain={-1.5:5}] (\x,{sin(\x^2 r)});
    \draw[blue!50!black, densely dotted] (-2,0) -- (5,0);
    \draw[black, densely dashed] (0,0) 
        -- ++(0,-2) node[below] {$x_1$} coordinate[pos=0] (A);
    \draw[black, densely dashed] (0.5,0) 
        -- ++(0,-2) node[below] {$x_2$} coordinate[pos=0] (B);
    \draw[black, densely dashed] (1.0,0) 
    -- ++(0,-2) node[below] {$x_2$} coordinate[pos=0] (B);
    \draw[black, densely dashed] (1.5,0) 
    -- ++(0,-2) node[below] {$x_2$} coordinate[pos=0] (B);
    \draw[black, densely dashed] (2.0,0) 
    -- ++(0,-2) node[below] {$x_2$} coordinate[pos=0] (B);

    \draw[thick, <->] (-2,4) 
        -- node[left, midway, anchor=south, rotate=90, font=\bfseries] (Y) {$f(x)$} (-2,-2)
        -- node[below, pos=1, font=\bfseries] {Quad. points} (5,-2);
  \end{scope}

\end{tikzpicture}

\end{document}

Answer 1

\documentclass[tikz, border=1cm]{standalone}
\tikzset{>=latex}
\begin{document}
\begin{tikzpicture}[
declare function={f(\x)=sin((\x-2)^2 r)+2;},
]
\draw[blue!50!black] plot[domain={0.5:7}, samples=50, smooth] (\x,{f(\x)});
\draw[blue!50!black, densely dotted] (0,2) -- (7,2);
\draw[densely dashed] (2.0,0) node[below]{$x_1$} -- +(0,{f(2.0)}) node[above=4pt]{$y_1$};
\draw[densely dashed] (2.5,0) node[below]{$x_2$} -- +(0,{f(2.5)}) node[above=4pt]{$y_2$};
\draw[densely dashed] (3.0,0) node[below]{$x_3$} -- +(0,{f(3.0)}) node[above=4pt]{$y_3$};
\draw[densely dashed] (3.5,0) node[below]{$x_4$} -- +(0,{f(3.5)}) node[above=4pt]{$y_4$};
\draw[densely dashed] (5.0,0) node[below]{$x_n$} -- +(0,{f(5.0)}) node[above right]{$y_n$};
\draw[thick, <->] (0,6) --node[above, rotate=90, font=\bfseries] (Y) {$f(x)$} (0,0) -- (7,0) node[below, font=\bfseries] {Quad. points};
\end{tikzpicture}
\end{document}

编辑：用一些随机点代替函数

\documentclass[tikz, border=1cm]{standalone}
\tikzset{>=latex}
\begin{document}
\begin{tikzpicture}
\begin{scope}
\draw[blue!50!black] plot[smooth] coordinates {(1.0,1.2) (1.5,2.3) (2.0,2.0) (2.5,3.0) (3.0,2.6) (3.5,1.8) (4.0,2.4) (5.0,1.5) (7.0,3.0)};
\draw[blue!50!black, densely dotted] (0,2) -- (7,2);
\draw[densely dashed] (2.0,0) node[below]{$x_1$} -- (2.0,2.0) node[above=4pt]{$y_1$};
\draw[densely dashed] (2.5,0) node[below]{$x_2$} -- (2.5,3.0) node[above=4pt]{$y_2$};
\draw[densely dashed] (3.0,0) node[below]{$x_3$} -- (3.0,2.6) node[above=4pt]{$y_3$};
\draw[densely dashed] (3.5,0) node[below]{$x_4$} -- (3.5,1.8) node[above=4pt]{$y_4$};
\draw[densely dashed] (5.0,0) node[below]{$x_n$} -- (5.0,1.5) node[above=4pt]{$y_n$};
\draw[thick, <->] (0,6) --node[above, rotate=90, font=\bfseries] (Y) {$f(x)$} (0,0) -- (7,0) node[below, font=\bfseries] {Quad. points};
\end{scope}
\end{tikzpicture}
\end{document}