为什么我的多功能图看上去不正确？

Question

\begin{align*}
        P(x) = 
        \begin{cases}
            \frac{\frac{1}{2}x^{2}}{4} & 0<x<2 \\
            \left(-\frac{\frac{1}{2}}{2}\left(\frac{x^{2}}{2}-4x\right)\right)-1 & 2<x<4\\
        \end{cases}
    \end{align*}
    \item[(c)] Graph $P(x)$.
    \begin{tikzpicture}
        \begin{axis}[
            legend pos=north west,
            axis x line=middle,
            axis y line=middle,
            grid = major,
            width=8cm,
            height=6cm,
            grid style={dashed, gray!30},
            xmin=0,     % start the diagram at this x-coordinate
            xmax=4,    % end   the diagram at this x-coordinate
            ymin= 0,     % start the diagram at this y-coordinate
            ymax= 1,   % end   the diagram at this y-coordinate
            y label style={at={(axis description cs:-0.2,0.5)},rotate=90,anchor=south},
            ylabel=$P(x)$,
            tick align=outside,
            minor tick num=-3,
            enlargelimits=false,
            tension=0.08]
            \addplot[smooth, black, domain=0:2] {((1/2)*((x)^2))/4};
            \addplot[smooth, black, domain=2:4] {((-.25)*(((x)^2)/2)-4(x))-1};
        \end{axis}
    \end{tikzpicture}

Answer 1

您在写第二个等式时犯了几个错误。首先， 中没有隐式乘法\pgfmath，因此您需要写4*x，而不是4x。

其次，你写了太多的括号，以至于它们配对错误：

代码：

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}[]
    \begin{axis}[
            legend pos=north west,
            axis x line=middle,
            axis y line=middle,
            grid = major,
            width=8cm,
            height=6cm,
            grid style={dashed, gray!30},
            xmin=0,     % start the diagram at this x-coordinate
            xmax=4,    % end   the diagram at this x-coordinate
            ymin= 0,     % start the diagram at this y-coordinate
            ymax= 1,   % end   the diagram at this y-coordinate
            y label style={at={(axis description cs:-0.2,0.5)},rotate=90,anchor=south},
            ylabel=$P(x)$,
            tick align=outside,
            minor tick num=-3,
            enlargelimits=false,
            tension=0.08]
            \addplot[black, domain=0:2] {1/8*(x)^2};
            \addplot[blue, domain=2:4] {-1/4*((x)^2/2 -4*x)-1};
        \end{axis}
\end{tikzpicture}
\end{document}

完成您需要的操作（请注意，这比您的代码更简洁，而且可编译……以供您下次发布问题时使用！）

Answer 2

解决方案是重现您问题中显示的图像，并使用更正和稍微优化的代码：

\documentclass[varwidth, border=3.141592]{standalone}
\usepackage{mathtools}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}

\begin{document}
    \[
P(x) = \begin{dcases}
        \dfrac{\frac{1}{2}x^{2}}{4} & 0<x<2 \\
       -\dfrac{\frac{1}{2}}{2}\biggl(\dfrac{x^{2}}{2} - 4x\biggr) -1 
                                    & 2<x<4
       \end{dcases}
    \]
    \begin{tikzpicture}
\begin{axis}[
    height=6cm, width=8cm,
    axis lines = left,
    legend pos = north west,
    grid,
    grid style={dashed, gray!30},
    ylabel=$P(x)$,
    tick align=outside,
    minor tick num=1,
    enlargelimits=false,
    tension=0.08,
    no marks,
            ]
\addplot +[thick, domain=0:2] {1/8*(x)^2};
\addplot +[thick, domain=2:4] {-1/4*((x)^2/2-4*x)-1};
    \legend{blue, red}
\end{axis}
    \end{tikzpicture}
\end{document}