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planet/沈浪熊猫儿/2021年浙江高考数学第七题函数曲线绘制.tm

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<TeXmacs|2.1.3>
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<doc-data|<doc-title|2021年浙江省高考数学第七题函数曲线绘制>>
2021年浙江省高考数学选择题第七题如下所示
<\framed>
7. 已知函数<math|f<around*|(|x|)>=x<rsup|2>+<frac|1|4>,g<around*|(|x|)>=sin
x>则图像为如图的函数可能是
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<\wide-tabular>
<tformat|<table|<row|<\cell>
A. <math|y=f<around*|(|x|)>+g<around*|(|x|)>-<frac|1|4>>
</cell>|<\cell>
B. <math|y=f<around*|(|x|)>-g<around*|(|x|)>-<frac|1|4>>
</cell>>|<row|<\cell>
C. <math|y=f<around*|(|x|)> g<around*|(|x|)>>
</cell>|<\cell>
D. <math|y=<frac|g<around*|(|x|)>|f<around*|(|x|)>>>
</cell>>>>
</wide-tabular>
</framed>
本文将从如何绘制<math|sin<around*|(|x|)>>开始讲解如何绘制题目中的选项D
<section*|插入<name|Gnuplot>会话>
本文使用<name|Gnuplot>来绘制函数曲线请提前安装好<name|Gnuplot>这个软件并保证在墨干编辑器中可以使用<name|Gnuplot>会话提示Windows平台除了安装<name|Gnuplot>之外还需要额外从Windows应用商店安装Python建议安装Python3.8.x
在墨干编辑器中使用<menu|Insert|Fold|Executable|Gnuplot>就可以插入一个<name|Gnuplot>会话
<\session|gnuplot|default>
<\output>
gnuplot 5.4 patchlevel 2
</output>
<\input>
gnuplot]\
<|input>
\;
</input>
</session>
<section*|绘制<math|sin<around*|(|x|)>>>
<\session|gnuplot|default>
<\unfolded-io>
gnuplot]\
<|unfolded-io>
% -width 0.618par
plot sin(x)
<|unfolded-io>
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</unfolded-io>
<\input>
gnuplot]\
<|input>
\;
</input>
</session>
不做任何配置直接绘制<math|sin<around*|(|x|)>>默认的图像不够友好
<section*|美化<math|sin<around*|(|x|)>>>
我们来逐步调整一下首先将上图的边框换成我们熟悉的坐标轴
<\session|gnuplot|default>
<\unfolded-io>
gnuplot]\
<|unfolded-io>
% -width 0.618par
<\with|color|red>
unset border
set zeroaxis linetype -1 linewidth 2
set xtics axis
set ytics axis
</with>
plot sin(x)
<|unfolded-io>
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</unfolded-io>
<\input>
gnuplot]\
<|input>
\;
</input>
</session>
<verbatim|unset border><\footnote>
http://gnuplot.info/docs_5.5/loc9713.html
</footnote>的作用是把外面的边框去掉<verbatim|zeroaxis><\footnote>
http://gnuplot.info/docs_5.5/loc16801.html
</footnote>可用于设置两个坐标轴都经过原点
通过上面四行配置我们得到一个在中学教育中经常使用到的函数曲线图像
可以再做一些调整让这个图像更加美观一些
<\session|gnuplot|default>
<\folded-io>
gnuplot]\
<|folded-io>
% -width 0.618par
unset border
set zeroaxis linetype -1 linewidth 2
set xtics axis
set ytics axis
\;
<\with|color|red>
set xtics pi
set ytics 1
set arrow from 0,0 to 10,0
set arrow from 0,0 to 0,1.5
</with>
\;
plot <with|color|red|[-10:10][-1.5:1.5]> sin(x)
<with|color|red|linecolor rgb "black">
<|folded-io>
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</folded-io>
<\input>
gnuplot]\
<|input>
\;
</input>
</session>
接下来新增的四行我们配置了<math|x>轴的刻度单位是<math|\<pi\>><math|y>轴的刻度单位是1然后绘制了两个箭头在最后的plot命令中设置了定义域为<math|<around*|[|-10:10|]>>值域为<math|<around*|[|-1.5:1.5|]>>最后把曲线颜色调整成了黑色
通过以上配置我们得到一个在中学教育中经常使用的函数曲线图像
<section*|绘制选项D>
我们选中上一个小节中的代码片段使用右键菜单复制然后使用右键菜单粘贴到下面的会话中修改plot命令里面的函数就可以绘制选项D的曲线在这个例子中我们稍稍调整一下刻度定义域值域以更加清楚地展示曲线的性质
<\session|gnuplot|default>
<\unfolded-io>
gnuplot]\
<|unfolded-io>
% -width 0.8par
unset border
set zeroaxis linetype -1 linewidth 2
set xtics axis
set ytics axis
\;
set xtics pi
set ytics 0.5
set arrow from 0,0 to 15,0
set arrow from 0,0 to 0,1.2
\;
plot [-15:15][-1.2:1.2] <with|color|red|(sin(x)/(x*x+1/4)) \\>
linecolor rgb "red" <with|color|red|linewidth 1.5>
<|unfolded-io>
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</unfolded-io>
<\input>
gnuplot]\
<|input>
\;
</input>
</session>
也可以在同一个段落里面绘制两个曲线如下所示
<\session|gnuplot|default>
<\unfolded-io>
gnuplot]\
<|unfolded-io>
% -width 0.8par
unset border
set zeroaxis linetype -1 linewidth 2
set xtics axis
set ytics axis
\;
set xtics pi
set ytics 0.5
set arrow from 0,0 to 15,0
set arrow from 0,0 to 0,1.2
\;
plot [-15:15][-1.2:1.2] \\
(sin(x)/(x*x+1/4)) linecolor rgb "red" linewidth 1.5<with|color|red|,>
\\
<with|color|red|sin(x) linecolor rgb "blue">
\;
<|unfolded-io>
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<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|绘制<with|mode|<quote|math>|sin<around*|(|x|)>>>
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