diff --git a/1.1-perpare/perpare.tex b/1.1-perpare/perpare.tex
index 40fd6a6..c33f188 100644
--- a/1.1-perpare/perpare.tex
+++ b/1.1-perpare/perpare.tex
@@ -150,8 +150,8 @@ $
然后画图:\bigskip
\begin{tikzpicture}[domain=-1:9.5]
- \draw[-latex](-1.5,0) -- (9.5,0) node[below]{$x-axis$};
- \draw[-latex](0,-1.5) -- (0, 1.5) node[above]{$y-axis$};
+ \draw[-latex](-1.5,0) -- (9.5,0) node[below]{$x$};
+ \draw[-latex](0,-1.5) -- (0, 1.5) node[above]{$y$};
\draw[very thin, gray, densely dashed](-1.5,1.5)grid(9.5,-1.5);
\draw [black, thick](-0.25,-1.5) -- (1,1);
\draw[black, thick,domain=1:9.5] plot (\x, {ln(sqrt(\x))});
@@ -235,9 +235,9 @@ $f(x+T)=f(x)$,其中T为周期。 \bigskip
$y=A$,A为常数,图像平行于x轴:
\begin{tikzpicture}[domain=-1:5]
- \draw[-latex](-1,0) -- (5,0) node[below]{$x-axis$};
- \draw[-latex](0,-0.5) -- (0, 1.5) node[above]{$y-axis$};
- \draw[black, thick](-1,1) -- (5,1) node[below]{$y=A$};
+ \draw[-latex](-1,0) -- (5,0) node[below]{$x$};
+ \draw[-latex](0,-0.5) -- (0, 1.5) node[above]{$y$};
+ \draw[black, thick](-1,1) -- (5,1) node[right]{$y=A$};
\end{tikzpicture}
\subparagraph{幂函数} \leavevmode \bigskip
@@ -245,13 +245,13 @@ $y=A$,A为常数,图像平行于x轴:
$y=x^{\mu}$,$\mu$为实数,当$x>0$,$y=x^{\mu}$都有定义:
\begin{tikzpicture}[scale=0.9]
- \draw[-latex](-2,0) -- (2,0) node[below]{$x-axis$};
- \draw[-latex](0,-2) -- (0,4) node[above]{$y-axis$};
- \draw[black, thick, domain=0.3:2] plot (\x,1/\x) node[below]{$\mu =-1$};
- \draw[black, thick, domain=-2:-0.5] plot (\x,1/\x) node[above]{$\mu =-1$};
- \draw[black, thick, domain=0.01:2] plot (\x, {sqrt(\x)}) node[below]{$\mu =\frac{1}{2}$};
- \draw[black, thick, domain=-2:2] plot (\x,\x) node[above]{$\mu =1$};
- \draw[black, thick, domain=-2:2] plot (\x, {\x*\x}) node[above]{$\mu =2$};
+ \draw[-latex](-2,0) -- (2,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,4) node[above]{$y$};
+ \draw[black, thick, domain=0.3:2] plot (\x,1/\x) node[right]{$\mu =-1$};
+ \draw[black, thick, domain=-2:-0.5] plot (\x,1/\x) node[right]{$\mu =-1$};
+ \draw[black, thick, domain=0.01:2] plot (\x, {sqrt(\x)}) node[right]{$\mu =\frac{1}{2}$};
+ \draw[black, thick, domain=-2:2] plot (\x,\x) node[right]{$\mu =1$};
+ \draw[black, thick, domain=-2:2] plot (\x, {\x*\x}) node[right]{$\mu =2$};
\end{tikzpicture}
所以对于幂函数,可以根据不同幂下相同单调性来研究最值:
@@ -268,10 +268,10 @@ $y=x^{\mu}$,$\mu$为实数,当$x>0$,$y=x^{\mu}$都有定义:
$y=a^x(a>0,a\neq 1)$:
\begin{tikzpicture}[scale=0.9]
- \draw[-latex](-2,0) -- (2,0) node[below]{$x-axis$};
- \draw[-latex](0,-0.5) -- (0,4) node[above]{$y-axis$};
- \draw[black, thick, domain=-2:2] plot (\x,{pow(1/2,\x)}) node at (-1.5,2){$01$};
+ \draw[-latex](-2,0) -- (2,0) node[below]{$x$};
+ \draw[-latex](0,-0.5) -- (0,4) node[above]{$y$};
+ \draw[black, thick, domain=-2:2] plot (\x,{pow(1/2,\x)}) node[right]{$01$};
\end{tikzpicture}
指数函数具有如下性质:
@@ -289,10 +289,10 @@ $y=a^x(a>0,a\neq 1)$:
$y=log_ax(a>0,a\neq 1)$为$y=a^x$的反函数:
\begin{tikzpicture}[scale=0.9]
- \draw[-latex](-0.5,0) -- (4,0) node[below]{$x-axis$};
- \draw[-latex](0,-2) -- (0,2) node[above]{$y-axis$};
- \draw[black, thick, domain=0.2:4] plot (\x,{ln(1/\x)}) node at (e,1.5){$01$};
+ \draw[-latex](-0.5,0) -- (4,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=0.2:4] plot (\x,{ln(1/\x)}) node[right]{$01$};
\end{tikzpicture}
对数函数具有如下性质:
@@ -311,44 +311,205 @@ $y=log_ax(a>0,a\neq 1)$为$y=a^x$的反函数:
正弦函数:
\begin{tikzpicture}[scale=0.9]
- \draw[-latex](-5,0) -- (5,0) node[below]{$x-axis$};
- \draw[-latex](0,-1.5) -- (0,2) node[above]{$y-axis$};
+ \draw[-latex](-5,0) -- (5,0) node[below]{$x$};
+ \draw[-latex](0,-1.5) -- (0,2) node[above]{$y$};
\draw[black, thick, domain=-5:5] plot (\x,{sin(\x r)}) node at (0,1.5){$\sin(x)$};
- \draw [black, densely dashed](-5,1) -- (5,1) node[below]{$x=1$};
- \draw [black, densely dashed](-5,-1) -- (5,-1) node[below]{$x=-1$};
+ \draw [black, densely dashed](-5,1) -- (5,1) node[right]{$x=1$};
+ \draw [black, densely dashed](-5,-1) -- (5,-1) node[right]{$x=-1$};
\draw [black, densely dashed](-pi/2*3,1) -- (-pi/2*3,0) node[below]{$-\frac{3\pi}{2}$};
- \draw [black, densely dashed](-pi,0) -- (-pi,0) node[below]{$-\pi$};
+ \draw [black](-pi,0) -- (-pi,0) node[below]{$-\pi$};
\draw [black, densely dashed](-pi/2,-1) -- (-pi/2,0) node[above]{$-\frac{\pi}{2}$};
- \draw [black, densely dashed](0,0) -- (0,0) node[above]{$0$};
+ \draw [black](0,0) -- (0,0) node[above]{$0$};
\draw [black, densely dashed](pi/2,1) -- (pi/2,0) node[below]{$\frac{\pi}{2}$};
- \draw [black, densely dashed](pi,0) -- (pi,0) node[below]{$\pi$};
+ \draw [black](pi,0) -- (pi,0) node[below]{$\pi$};
\end{tikzpicture}
余弦函数:
\begin{tikzpicture}[scale=0.9]
- \draw[-latex](-5,0) -- (5,0) node[below]{$x-axis$};
- \draw[-latex](0,-1.5) -- (0,2) node[above]{$y-axis$};
- \draw[black, thick, domain=-5:5] plot (\x,{cos(\x r)}) node at (0,1.5){$\sin(x)$};
- \draw [black, densely dashed](-5,1) -- (5,1) node[below]{$x=1$};
- \draw [black, densely dashed](-5,-1) -- (5,-1) node[below]{$x=-1$};
- \draw [black, densely dashed](-pi/2*3,0) -- (-pi/2*3,0) node[below]{$-\frac{3\pi}{2}$};
+ \draw[-latex](-5,0) -- (5,0) node[below]{$x$};
+ \draw[-latex](0,-1.5) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=-5:5] plot (\x,{cos(\x r)}) node at (0,1.5){$\cos(x)$};
+ \draw [black, densely dashed](-5,1) -- (5,1) node[right]{$x=1$};
+ \draw [black, densely dashed](-5,-1) -- (5,-1) node[right]{$x=-1$};
+ \draw [black](-pi/2*3,0) -- (-pi/2*3,0) node[below]{$-\frac{3\pi}{2}$};
\draw [black, densely dashed](-pi,-1) -- (-pi,0) node[above]{$-\pi$};
- \draw [black, densely dashed](-pi/2,0) -- (-pi/2,0) node[below]{$-\frac{\pi}{2}$};
+ \draw [black](-pi/2,0) -- (-pi/2,0) node[below]{$-\frac{\pi}{2}$};
\draw [black, densely dashed](0,1) -- (0,0) node[below]{$0$};
- \draw [black, densely dashed](pi/2,0) -- (pi/2,0) node[below]{$\frac{\pi}{2}$};
+ \draw [black](pi/2,0) -- (pi/2,0) node[below]{$\frac{\pi}{2}$};
\draw [black, densely dashed](pi,-1) -- (pi,0) node[above]{$\pi$};
\end{tikzpicture}
+弦函数有如下特征:
+
+\begin{enumerate}
+ \item 特殊函数值:$\sin 0=0$,$\sin\frac{\pi}{6}=\frac{1}{2}$,$\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$,$\sin\frac{\pi}{3}=\frac{\sqrt{3}}{2}$,$\sin\frac{\pi}{2}=1$,$\sin\pi=0$,$\sin\frac{3\pi}{2}=-1$,$\sin 2\pi=0$,$\cos 0=1$,$\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$,$\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$,$\cos\frac{\pi}{3}=\frac{1}{2}$,$\cos\frac{\pi}{2}=0$,$\cos\pi=-1$,$\cos\frac{3\pi}{2}=0$,$\cos 2\pi=1$。
+ \item 定义域:$(-\infty, +\infty)$,值域:$[-1,+1]$。
+ \item 奇偶性:$y=\sin x$为奇函数,$y=\cos x$为偶函数。
+ \item 周期性:最小正周期为$2\pi$。
+ \item 有界性:$\vert\sin x\vert\leqslant 1$,$\vert\cos x\vert\leqslant 1$。
+\end{enumerate}
+
+正切函数:
+
+\begin{tikzpicture}[scale=0.7]
+ \draw[-latex](-6,0) -- (6,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=-pi/2+0.5:pi/2-0.5] plot (\x,{tan(\x r)}) node[above]{$\tan(x)$};
+ \draw [black](0,0) -- (0,0) node[below]{$0$};
+ \draw[black, densely dashed](pi/2,2) -- (pi/2,-2);
+ \draw[black](pi/2,0) -- (pi/2,0) node at (pi/2+0.5,-0.5){$\frac{\pi}{2}$};
+ \draw[black, densely dashed](-pi/2,2) -- (-pi/2,-2);
+ \draw[black](-pi/2,0) -- (-pi/2,0) node at (-pi/2-0.5,-0.5){$-\frac{\pi}{2}$};
+ \draw[black, thick, domain=-pi/2*3+0.5:-pi/2-0.5] plot (\x,{tan(\x r)}) node[above]{$\tan(x)$};
+ \draw[black, densely dashed](pi/2*3,2) -- (pi/2*3,-2);
+ \draw[black](pi/2*3,0) -- (pi/2*3,0) node at (pi/2*3+0.5,-0.5){$\frac{3\pi}{2}$};
+ \draw[black, thick, domain=pi/2+0.5:pi/2*3-0.5] plot (\x,{tan(\x r)}) node[above]{$\tan(x)$};
+ \draw[black, densely dashed](-pi/2*3,2) -- (-pi/2*3,-2);
+ \draw[black](-pi/2*3,0) -- (-pi/2*3,0) node at (-pi/2*3-0.5,-0.5){$-\frac{3\pi}{2}$};
+\end{tikzpicture}
+
+余切函数:
+
+\begin{tikzpicture}[scale=0.7]
+ \draw[-latex](-4,0) -- (4,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=0.5:pi-0.5] plot (\x,{cot(\x r)}) node at(pi-1,2){$\cot(x)$};
+ \draw [black](0,0) -- (0,0) node[below]{$0$};
+ \draw[black](pi/2,0) -- (pi/2,0) node[below]{$\frac{\pi}{2}$};
+ \draw[black, densely dashed](pi,2) -- (pi,-2);
+ \draw[black](pi,0) -- (pi,0) node at (pi+0.5,-0.5){$\pi$};
+ \draw[black, thick, domain=-0.5:-pi+0.5] plot (\x,{cot(\x r)}) node at(-1,2){$\cot(x)$};
+ \draw[black](-pi/2,0) -- (-pi/2,0) node[below]{$-\frac{\pi}{2}$};
+ \draw[black, densely dashed](-pi,2) -- (-pi,-2);
+ \draw[black](-pi,0) -- (-pi,0) node at (-pi-0.5,-0.5){$-\pi$};
+\end{tikzpicture}
+
+切函数有如下特征:
+
+\begin{enumerate}
+ \item 特殊函数值:$\tan 0=0$,$\tan\frac{\pi}{6}=\frac{\sqrt{3}}{3}$,$\tan\frac{\pi}{4}=1$,$\tan\frac{\pi}{3}=\sqrt{3}$,$\lim_{x\to\frac{\pi}{2}}\tan x=\infty$,$\tan\pi=0$,$\lim_{x\to\frac{3\pi}{2}}\tan x=\infty$,$\tan 2\pi=0$,$\lim_{x\to 0}\cot x=\infty$,$\cot\frac{\pi}{6}=\sqrt{3}$,$\cot\frac{\pi}{4}=1$,$\cot\frac{\pi}{3}=\frac{\sqrt{3}}{3}$,$\cot\frac{\pi}{2}=0$,$\lim_{x\to\pi}\cot x=\infty$,$\cot\frac{3\pi}{2}=0$,$\lim_{x\to 2\pi}\cot x=\infty$。
+ \item 定义域:$\tan x:x\neq k\pi+\frac{\pi}{2}(k\in Z)$,$\cot x:x\neq k\pi(k\in Z)$,值域:$(-\infty,+\infty)$。
+ \item 奇偶性:定义域内均为奇函数。
+ \item 周期性:最小正周期为$\pi$。
+\end{enumerate}
+
+$$
+\sec x=\frac{1}{\cos x},\csc x=\frac{1}{\sin x}
+$$
+
+正割函数:
+
+\begin{tikzpicture}[scale=0.6]
+ \draw[-latex](-6,0) -- (6,0) node[below]{$x$};
+ \draw[-latex](0,-3) -- (0,3) node[above]{$y$};
+ \draw[black, thick, domain=-pi/2+0.4:pi/2-0.4] plot (\x,{sec(\x r)}) node[above]{$\sec(x)$};
+ \draw[black, thick, domain=-pi/2*3+0.4:-pi/2-0.4] plot (\x,{sec(\x r)}) node[below]{$\sec(x)$};
+ \draw[black, thick, domain=pi/2+0.4:pi/2*3-0.4] plot (\x,{sec(\x r)}) node[below]{$\sec(x)$};
+ \draw[black, thick, domain=-pi*2:-pi/2*3-0.4] plot (\x,{sec(\x r)}) node[above]{$\sec(x)$};
+ \draw[black, thick, domain=pi/2*3+0.4:pi*2] plot (\x,{sec(\x r)}) node at (pi*2,3){$\sec(x)$};
+ \draw[black, densely dashed](-6,1) -- (6,1);
+ \draw[black, densely dashed](-6,-1) -- (6,-1);
+ \draw[black, densely dashed](-pi/2*3,3) -- (-pi/2*3,-3);
+ \draw[black, densely dashed](-pi/2,3) -- (-pi/2,-3);
+ \draw[black, densely dashed](pi/2,3) -- (pi/2,-3);
+ \draw[black, densely dashed](pi/2*3,3) -- (pi/2*3,-3);
+ \draw[black](0,0) -- (0,0) node[below]{$0$};
+ \draw[black](0,1) -- (0,1) node at(0.5,0.5){$1$};
+ \draw[black](0,-1) -- (0,-1) node at(0.5,-1.5){$-1$};
+ \draw[black](-pi/2*3,0) -- (-pi/2*3,0) node at(-pi/2*3-0.5,-0.5){$-\frac{3\pi}{2}$};
+ \draw[black](-pi/2,0) -- (-pi/2,0) node at(-pi/2-0.5,-0.5){$-\frac{\pi}{2}$};
+ \draw[black](pi/2,0) -- (pi/2,0) node at(pi/2+0.5,-0.5){$\frac{\pi}{2}$};
+ \draw[black](pi/2*3,0) -- (pi/2*3,0) node at(pi/2*3+0.5,-0.5){$\frac{3\pi}{2}$};
+\end{tikzpicture}
+
+余割函数:
+
+\begin{tikzpicture}[scale=0.6]
+ \draw[-latex](-7,0) -- (7,0) node[below]{$x$};
+ \draw[-latex](0,-3) -- (0,3) node[above]{$y$};
+ \draw[black, thick, domain=0.4:pi-0.4] plot (\x,{1/sin(\x r)}) node[above]{$\csc(x)$};
+ \draw[black, thick, domain=pi+0.4:pi*2-0.4] plot (\x,{1/sin(\x r)}) node[below]{$\csc(x)$};
+ \draw[black, thick, domain=-pi+0.4:-0.4] plot (\x,{1/sin(\x r)}) node[below]{$\csc(x)$};
+ \draw[black, thick, domain=-pi*2+0.4:-pi-0.4] plot (\x,{1/sin(\x r)}) node[above]{$\csc(x)$};
+ \draw[black, densely dashed](-7,1) -- (7,1);
+ \draw[black, densely dashed](-7,-1) -- (7,-1);
+ \draw[black, densely dashed](-pi,3) -- (-pi,-3);
+ \draw[black, densely dashed](-pi*2,3) -- (-pi*2,-3);
+ \draw[black, densely dashed](pi,3) -- (pi,-3);
+ \draw[black, densely dashed](pi*2,3) -- (pi*2,-3);
+ \draw[black](0,0) -- (0,0) node[below]{$0$};
+ \draw[black](0,1) -- (0,1) node at(0.5,0.5){$1$};
+ \draw[black](0,-1) -- (0,-1) node at(0.5,-1.5){$-1$};
+ \draw[black](-pi,0) -- (-pi,0) node at(-pi-0.5,-0.5){$\pi$};
+ \draw[black](-pi*2,0) -- (-pi*2,0) node at(-pi*2+0.5,-0.5){$2\pi$};
+ \draw[black](pi,0) -- (pi,0) node at(pi+0.5,-0.5){$\pi$};
+ \draw[black](pi*2,0) -- (pi*2,0) node at(pi*2-0.5,-0.5){$2\pi$};
+\end{tikzpicture}
+
+割函数有如下特征:
+
+\begin{enumerate}
+ \item 定义域:$\sec x:x\neq k\pi+\frac{\pi}{2}(k\in Z)$,$\csc x:x\neq k\pi(k\in Z)$,值域:$(-\infty,-1]\cup [1,+\infty)$。
+ \item 奇偶性:$y=\sec x$为偶函数,$y=\csc x$为奇函数。
+ \item 周期性:最小正周期为$2\pi$。
+\end{enumerate}
+
\subparagraph{反三角函数} \leavevmode \bigskip
反正弦函数:
\begin{tikzpicture}
- \draw[-latex](-1.5,0) -- (1.5,0) node[below]{$x-axis$};
- \draw[-latex](0,-2) -- (0,2) node[above]{$y-axis$};
- % \draw[black, thick, domain=-1:1] plot (\x,{arcsin(\x r)}) node at (1,pi/2){$\arcsin(x)$};
- \draw[domain=-1:1,smooth,variable=\y] plot ({rad(asin(\y))},\y) node[right] {$x = \arcsin y$};
+ \draw[-latex](-1.5,0) -- (1.5,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=-1:1] plot (\x,{rad(asin(\x))}) node[right]{$\arcsin(x)$};
+ \draw [black, densely dashed](1,pi/2) -- (0,pi/2) node[left]{$\frac{\pi}{2}$};
+ \draw [black](0,0) -- (0,0) node[below]{$0$};
+ \draw [black, densely dashed](1,pi/2) -- (1,0) node[below]{$1$};
+ \draw [black, densely dashed](-1,-pi/2) -- (0,-pi/2) node[right]{$-\frac{\pi}{2}$};
+ \draw [black, densely dashed](-1,-pi/2) -- (-1,0) node[above]{$-1$};
+\end{tikzpicture}
+
+反余弦函数:
+
+\begin{tikzpicture}
+ \draw[-latex](-1.5,0) -- (1.5,0) node[below]{$x$};
+ \draw[-latex](0,-0.5) -- (0,4) node[above]{$y$};
+ \draw[black, thick, domain=-1:1] plot (\x,{rad(acos(\x)}) node at (-2, pi){$\arccos(x)$};
+ \draw [black, densely dashed](0,pi/2) -- (0,pi/2) node[left]{$\frac{\pi}{2}$};
+ \draw [black, densely dashed](1,0) -- (1,0) node[below]{$1$};
+ \draw [black, densely dashed](-1,pi) -- (0,pi) node[right]{$\pi$};
+ \draw [black, densely dashed](-1,pi) -- (-1,0) node[above]{$-1$};
+\end{tikzpicture}
+
+反弦函数有如下特征:
+
+\begin{enumerate}
+ \item 特殊函数值:$\arcsin 0=0$,$\arcsin\frac{1}{2}=\frac{\pi}{6}$,$\arcsin\frac{\sqrt{2}}{2}=\frac{\pi}{4}$,$\arcsin\frac{\sqrt{3}}{2}=\frac{\pi}{3}$,$\arcsin 1=\frac{\pi}{2}$,$\arccos 1=0$,$\arccos\frac{\sqrt{3}}{2}=\frac{\pi}{6}$,$\arccos\frac{\sqrt{2}}{2}=\frac{\pi}{4}$,$\arccos\frac{1}{2}=\frac{\pi}{3}$,$\arccos 0=\frac{\pi}{2}$。
+ \item 定义域:$(-1, +1)$,值域:$\arcsin x:[-\frac{\pi}{2},+\frac{\pi}{2}]$,$\arccos x:[0,\pi]$。
+ \item 单调性:$y=\arcsin x$单调增,$y=\arccos x$单调减
+ \item 奇偶性:$y=\arcsin x$为奇函数。
+ \item 有界性:$\vert\arcsin x\vert\leqslant\frac{\pi}{2}$,$0\leqslant\arccos x\leqslant\pi$。
+ \item 性质:$\arcsin x+\arccos x=\frac{\pi}{2}(-1\leqslant x\leqslant 1)$
+\end{enumerate}
+
+对反弦函数性质进行证明:
+
+令$f(x)=\arcsin x+\arccos x$,对其求导得:$f'(x)=\frac{1}{\sqrt{1-x^2}}-\frac{1}{1-x^2}=0$,所以$f(x)$是个常数函数。
+
+又$f(0)=\frac{\pi}{2}$,所以该函数等于$\frac{\pi}{2}$。
+
+反正切函数:
+
+\begin{tikzpicture}[scale=0.9]
+ \draw[-latex](-3,0) -- (3,0) node[below]{$x$};
+ \draw[-latex](0,-2) -- (0,2) node[above]{$y$};
+ \draw[black, thick, domain=-3:3] plot (\x,{rad(atan(\x))}) node[right]{$\arcsin(x)$};
+ \draw [black, densely dashed](-3,pi/2) -- (3,pi/2) node[right]{$\frac{\pi}{2}$};
+ % \draw [black](0,0) -- (0,0) node[below]{$0$};
+ % \draw [black, densely dashed](1,pi/2) -- (1,0) node[below]{$1$};
+ % \draw [black, densely dashed](-1,-pi/2) -- (0,-pi/2) node[right]{$-\frac{\pi}{2}$};
+ % \draw [black, densely dashed](-1,-pi/2) -- (-1,0) node[above]{$-1$};
\end{tikzpicture}
\paragraph{分段函数}