14

Can you help me with my page of function graphs? I could make the first four graphs but there is a problem with plotting by others. All graphs should have the same size like the first four ones. Thank you!

\documentclass{article}
\usepackage{pgfplots}
\usepackage{subfigure}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,calc,arrows,decorations.markings,decorations.pathmorphing}
\newcommand{\tg}{\mathop{\mathrm{tg}}}
\newcommand{\cotg}{\mathop{\mathrm{cotg}}}
\newcommand{\arctg}{\mathop{\mathrm{arctg}}}
\newcommand{\arccotg}{\mathop{\mathrm{arccotg}}}
\begin{document}
\begin{figure}[H] 
\centering  
\subfigure
{
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{1}) node[above] {$y=c$};
 \end{tikzpicture}
}
%
{  
  \begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=x$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x*\x}) node[above] {$y=x^2$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
       \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.15:1.15] plot (\x,{\x*\x*\x}) node[above]     {$y=x^3$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=\frac{1}{x}$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]     {$y=\sqrt{x}$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=e^x$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};    
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=\ln{x}$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=\sin(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=\cos(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above] {$y=\tg(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]    {$y=\cotg(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
       \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]    {$y=\arcsin(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]    {$y=\arccos(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]    {$y=\arctg(x)$};
  \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}[smooth,scale=0.8]
        \draw[thick,->] (-2,0) -- (2,0) node[below] {$x$};
        \draw[thick,->] (0,-1.5) -- (0,1.5) node[right] {$y$};
        \draw[blue,thick,domain=-1.5:1.5] plot (\x,{\x}) node[above]    {$y=\arccotg(x)$};
  \end{tikzpicture}
}
\end{figure}
\end{document}

graphs

goLK
  • 793

3 Answers3

17

For this kind of drawings I would suggest you to use pgfplots instead; the inverse trigonometric functions pose a challenge to the PGF math engine, so you can use gnuplot. Here's a big part of your image; the missing elements are easy to fill in:

\documentclass{article}
\usepackage{pgfplots}
\usepackage{subfigure}

\newcommand{\tg}{\mathop{\mathrm{tg}}}
\newcommand{\cotg}{\mathop{\mathrm{cotg}}}
\newcommand{\arctg}{\mathop{\mathrm{arctg}}}
\newcommand{\arccotg}{\mathop{\mathrm{arccotg}}}

\pgfplotsset{
compat=1.8,
every axis plot/.append style={
  no marks,
  blue,
  thick
  },
every axis/.style={
  enlargelimits=false,
  axis lines=middle,
  xticklabels=empty,
  yticklabels=empty,
  xtick=\empty,
  ytick=\empty,
  width=4.75cm,
  xlabel style={at={(rel axis cs:0.94,0.48)},anchor=north west},
  ylabel style={at={(rel axis cs:0.5,1.01)},anchor=east},
  xlabel=$\scriptstyle x$,
  ylabel=$\scriptstyle  y$
  },
legend style={
  draw=none,
  font=\footnotesize\color{blue}
  },
every axis legend/.append style={
  at={(0.55,1.15)},
  anchor=north west
  },
empty legend
}

\begin{document}

\begin{figure}
\centering  
\subfigure
{%
\begin{tikzpicture}
\begin{axis}[ymin=-1.5,ymax=1.5]
\addplot+[domain=-1.5:1.5] {1};
\addlegendentry{$f(x)=c$}
\end{axis}
\end{tikzpicture}
}
\subfigure%
{  
\begin{tikzpicture}
\begin{axis}
\addplot+[domain=-1.5:1.5] {x};
\addlegendentry{$f(x)=x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[ymin=-1.5,ymax=1.5]
\addplot+[domain=-3:3,samples=101] {x^(2)};
\addlegendentry{$f(x)=x^2$}
\end{axis}
\end{tikzpicture}
}\\
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[ymin=-1.5,ymax=1.5]
\addplot+[domain=-1.5:1.5] {x^(3)};
\addlegendentry{$f(x)=x^3$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}
\addplot+[domain=-1.5:1.5,unbounded coords=jump,samples=101] {x^(-1)};
\addlegendentry{$f(x)=x^{-1}$}
\end{axis}
 \end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-1.5,ymin=-1.5,ymax=1.5]
\addplot+[domain=0.0001:1.5,unbounded coords=jump,samples=301] {x^(0.5)};
\addlegendentry{$f(x)=\sqrt{x}$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[samples=101] {e^(x)};
\addlegendentry{$f(x)=e^{x}$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[domain=-1.5:1.5,unbounded coords=jump,samples=301] {ln(x)};
\addlegendentry{$f(x)=\ln{x}$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-6.283,xmax=6.28,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[] gnuplot [domain=-6.283:6.283,samples=105] {sin(x)};
\addlegendentry{$f(x)=\sin x$}
\end{axis}
\end{tikzpicture}
}\\
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-6.283,xmax=6.28,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[] gnuplot [domain=-6.283:6.283,samples=105] {cos(x)};
\addlegendentry{$f(x)=\cos x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-3.5,xmax=3.5,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[] gnuplot [domain=-1.5:1.5,unbounded coords=jump,samples=105] {tan(x)};
\addplot+[blue] gnuplot [domain=-3.5:-1.8,unbounded coords=jump,samples=105] {tan(x)};
\addplot+[blue] gnuplot [domain=1.8:3.5,unbounded coords=jump,samples=105] {tan(x)};
\addlegendentry{$f(x)=\tg x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-3,xmax=3,ymin=-1.5,ymax=1.5,enlargelimits=true]
\addplot+[domain=-3:-0.1,unbounded coords=jump,samples=101] {cot(deg(x))};
\addplot+[blue,domain=0.1:3,unbounded coords=jump,samples=101] {cot(deg(x))};
\addlegendentry{$f(x)=\cotg x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-1,xmax=1,ymin=-1,ymax=1,enlargelimits=true]
\addplot+[] gnuplot [domain=-1:1,unbounded coords=jump,samples=120] {asin(x)};
\addlegendentry{$f(x)=\arcsin x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-1,xmax=1,ymin=-3,ymax=3,enlargelimits=true]
\addplot+[] gnuplot [domain=-1:1,unbounded coords=jump,samples=120] {acos(x)};
\addlegendentry{$f(x)=\arccos x$}
\end{axis}
\end{tikzpicture}
}
%
\subfigure
{  
\begin{tikzpicture}
\begin{axis}[xmin=-8,xmax=8,ymin=-1.2,ymax=1.2,enlargelimits=true]
\addplot+[] gnuplot [domain=-8:8,unbounded coords=jump,samples=120] {atan(x)};
\addlegendentry{$f(x)=\arctg x$}
\end{axis}
\end{tikzpicture}
}
%
\end{figure}

\end{document}

enter image description here

Since gnuplot is being used, you need to have it installed in your system, and the document has to be processed using 

pdflatex --shell-escape name.tex

in Lynux systems or something like 

pdflatex enable-write18 name.tex

in Windows.

By the way, subfigure is an obsolete package; you should use subfig or subcaption instead.

Moriambar
  • 11,466
Gonzalo Medina
  • 505,128
12

This is another approach which uses the groupplots library of »pgfplots« to group the plots in some kind of grid. It needs exactly the same prerequisites as Gonzalo's answer.

\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{geometry}
\usepackage{mathtools}
\usepackage{pgfplots}
\usepgfplotslibrary{groupplots}

\DeclareMathOperator{\tg}{tg}
\DeclareMathOperator{\cotg}{cotg}
\DeclareMathOperator{\arctg}{arctg}
\DeclareMathOperator{\arccotg}{arccotg}

\pgfplotsset{compat=newest}

\begin{document}
  \begin{tikzpicture}
    \begin{groupplot}[
      group style={
        group size=4 by 4,
        vertical sep=1.5cm
      },
      height=4cm,
      width=4cm,
      restrict y to domain=-4:4,
      samples=100,
      axis x line=middle,
      axis y line=middle,
      xmin=-4,
      xmax=4,
      xtick=\empty,
      ymin=-4,
      ymax=4,
      ytick=\empty
    ]
      \nextgroupplot[title={$y=c$}]
      \addplot[blue,smooth] {1};
      \nextgroupplot[title={$y=x$}]
      \addplot[blue,smooth] {x};
      \nextgroupplot[title={$y=x^2$}]
      \addplot[blue,smooth] {x^2};
      \nextgroupplot[title={$y=x^3$}]
      \addplot[blue,smooth] {x^3};

      \nextgroupplot[title={$y=\frac{1}{x}$}]
      \addplot[blue,smooth] {1/x};
      \nextgroupplot[title={$y=\sqrt{x}$}]
      \addplot[blue,smooth,domain=0:4] {sqrt(x)};
      \nextgroupplot[title={$y=e^x$}]
      \addplot[blue,smooth] {exp(x)};
      \nextgroupplot[title={$y=\ln x$}]
      \addplot[blue,smooth,domain=0.1:4] {ln(x)};

      \nextgroupplot[title={$y=\sin x$}]
      \addplot[blue,smooth] {sin(deg(x))};
      \nextgroupplot[title={$y=\cos x$}]
      \addplot[blue,smooth] {cos(deg(x))};
      \nextgroupplot[title={$y=\tg x$}]
      \addplot[blue,smooth] {tan(deg(x))};
      \nextgroupplot[title={$y=\cotg x$}]
      \addplot[blue,smooth] {cot(deg(x))};;

      \nextgroupplot[title={$y=\arcsin x$}]
      \addplot[blue,smooth] gnuplot[domain=-1:1,unbounded coords=jump] {asin(x)};
      \nextgroupplot[title={$y=\arccos x$}]
      \addplot[blue,smooth] gnuplot[domain=-1:1,unbounded coords=jump] {acos(x)};
      \nextgroupplot[title={$y=\arctg x$}]
      \addplot[blue,smooth] gnuplot[domain=-4:4,unbounded coords=jump] {atan(x)};
      \nextgroupplot[title={$y=\arccotg x$}]
      \addplot[blue,smooth] gnuplot[domain=-4:4,unbounded coords=jump] {pi/2-atan(x)};
    \end{groupplot}
  \end{tikzpicture}
\end{document}

Modifications to the domains are left to the interested reader.

enter image description here

Community
  • 1
Thorsten Donig
  • 46,014
10

And for didactic purposes, here is a PSTricks version, which doesn't need gnuplot for plotting:

\documentclass{article}
\usepackage[margin=0.5cm]{geometry}
\usepackage{pst-plot}
\colorlet{graphcolor}{blue}
\newpsstyle{Graph}{linecolor=graphcolor, linewidth=2\pslinewidth}
\newpsstyle{legendstyle}{linestyle=none}
\makeatletter
\def\pslegend@iii[#1](#2){\rput[#1](#2){%
    \color{graphcolor}\pslegend@text}\gdef\pslegend@text{}}
\makeatother

\newcommand{\tg}{\mathop{\mathrm{tg}}}
\newcommand{\cotg}{\mathop{\mathrm{cotg}}}
\newcommand{\arctg}{\mathop{\mathrm{arctg}}}
\newcommand{\arccotg}{\mathop{\mathrm{arccotg}}}

\thispagestyle{empty}

\begin{document}
\psset{algebraic, labels=none, ticks=none}

\pslegend[tr]{$y = c$}
\begin{psgraph}[arrows=->](0,0)(-1,-1)(1,1){3.5cm}{3.5cm}
\psplot[style=Graph]{-1}{1}{0.7}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr](10,0){$y = x$}
\begin{psgraph}[arrows=->](0,0)(-1,-1)(1,1){3.5cm}{3.5cm}
\psplot[style=Graph]{-1}{1}{x}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = x^2$}
\begin{psgraph}[arrows=->](0,0)(-1,-1)(1,1){3.5cm}{3.5cm}
\psplot[style=Graph]{-1}{1}{x^2}
\end{psgraph}

\vspace*{1cm}
\pslegend[tr]{$y = x^3$}
\begin{psgraph}[arrows=->](0,0)(-1,-1)(1,1){3.5cm}{3.5cm}
\psplot[style=Graph]{-1}{1}{x^3}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \frac{1}{x}$}
\begin{psgraph}[arrows=->](0,0)(-5,-5)(5,5){3.5cm}{3.5cm}
\psplot[style=Graph]{0.2}{5}{1/x}
\psplot[style=Graph]{-5}{-0.2}{1/x}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \sqrt{x}$}
\begin{psgraph}[arrows=->](0,0)(-1,-1.5)(1,1.5){3.5cm}{3.5cm}
\psplot[style=Graph]{0}{1}{sqrt(x)}
\end{psgraph}

\vspace*{1cm}
\pslegend[tr]{$y = \mathrm{e}^x$}
\begin{psgraph}[arrows=->](0,0)(-2,-2)(2,2){3.5cm}{3.5cm}
\psplot[style=Graph]{-2}{0.6}{Euler^x}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \ln x$}
\begin{psgraph}[arrows=->](0,0)(-3,-3)(3,3){3.5cm}{3.5cm}
\psplot[style=Graph]{0.1}{3}{ln(x)}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \sin x$}
\begin{psgraph}[arrows=->](0,0)(-\psPiTwo,-1.5)(\psPiTwo,1.5){3.5cm}{3.5cm}
\psplot[style=Graph]{-\psPiTwo}{\psPiTwo}{sin(x)}
\end{psgraph}

\vspace*{1cm}
\pslegend[tr]{$y = \cos x$}
\begin{psgraph}[arrows=->](0,0)(-\psPiTwo,-1.5)(\psPiTwo,1.5){3.5cm}{3.5cm}
\psplot[style=Graph]{-\psPiTwo}{\psPiTwo}{cos(x)}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \tg x$}
\begin{psgraph}[arrows=->](0,0)(-3.5,-3.5)(3.5,3.5){3.5cm}{3.5cm}
\psplot[style=Graph]{-3.5}{-1.93}{tan(x)}
\psplot[style=Graph]{-1.2}{1.2}{tan(x)}
\psplot[style=Graph]{1.93}{3.5}{tan(x)}

\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr]{$y = \cotg x$}
\begin{psgraph}[arrows=->](0,0)(-\psPi,-5)(\psPi,5){3.5cm}{3.5cm}
\psplot[style=Graph]{-2.88}{-0.26}{1/tan(x)}
\psplot[style=Graph]{0.26}{2.88}{1/tan(x)}
\end{psgraph}

\vspace*{1cm}
\pslegend[tr](-10,0){$y = \arcsin x$}
\begin{psgraph}[arrows=->](0,0)(-1,-2)(1,2){3.5cm}{3.5cm}
\psplot[style=Graph, plotpoints=500]{-1}{1}{asin(x)}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr](-5,0){$y = \arccos x$}
\begin{psgraph}[arrows=->](0,0)(-1,-4)(1,4){3.5cm}{3.5cm}
\psplot[style=Graph, plotpoints=500]{-1}{1}{acos(x)}
\end{psgraph}%


\vspace*{1cm}%
%
\pslegend[tr](-5,0){$y = \arctg x$}
\begin{psgraph}[arrows=->](0,0)(-3,-3.5)(3,3.5){3.5cm}{3.5cm}
\psplot[style=Graph]{-3}{3}{atg(x)}
\end{psgraph}%
%
\hspace*{1cm}%
%
\pslegend[tr](-5,0){$y = \arccotg x$}
\begin{psgraph}[arrows=->](0,0)(-3,-3.5)(3,3.5){3.5cm}{3.5cm}
\psplot[style=Graph]{-3}{3}{PiDiv2-atg(x)}
\end{psgraph}
\end{document}

enter image description here

Christoph
  • 16,593
  • 1
  • 23
  • 47