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How can I plot a curve with a vertical and oblique asymptote, same as the following picture?

Curve equation: y=\sqrt[3]{\frac{x^7+3x^6-2x^5-x^4-3x^2+1}{x^4-2x^2}}

enter image description here

quark67
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H. Zadeh
  • 11
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    Welcome to TeX-SE! You can achieve this e.g. with pgfplots. What have you tried? –  Mar 15 '19 at 02:57
  • I was looking in the pgfplots gallery for some example that looked like what you're asking, but I didn't find anything like that, however you can check for yourself if you want.

    Nevertheless I don't understand your question, you can graph those kind of equations in the software you prefer and place the image in your LaTeX document.

     – Aradnix Mar 15 '19 at 03:01
  • you're right. But I dont know which software can do exactly the same thing that I showed by the picture. – H. Zadeh Mar 15 '19 at 03:14
  • @MaryamAmini You drew the figure with a software, didn't you? Then you can include this figure to your document, or use the software to export your figure to a TikZ or Asymptote code. –  Mar 15 '19 at 03:52

2 Answers2

4

It is true that you can draw the figure with other software and this has certainly some advantages. But you can also draw it with LaTeX, and then you do not have to worry to add equations to it. Here is an extended discussion of this topic.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[declare function={%
    f(\x)=pow((x^7+3*x^6-2*x^5-x^4-3*x^2+1)/(x^4-2*x^2),1/3);}]
  \begin{axis}[xmin=0,xmax=5,ymin=-0.5,ymax=6,xlabel={$x$},ylabel={$y$},grid=major,
   title={$\displaystyle f(x)=\sqrt[3]{\frac{x^7+3x^6-2x^5-x^4-3x^2+1}{x^4-2x^2}}$}]
    \addplot[color=blue,semithick,domain={sqrt(2.035)}:5,samples=71] {f(x)}
    node[pos=0.75,above,sloped]{$y=f(x)$};
    \addplot[color=blue,semithick,domain=0.55:1.11,samples=71] {f(x)};
    \addplot[color=green!70!black,domain=0:5,samples=2] {x}
    node[midway,below,sloped]{$y=x$};
    \addplot[color=green!70!black,domain=-0.5:6,samples=2] ({sqrt(2)},{x})
    node[midway,above,sloped]{$x=\sqrt{2}$};
    \addplot[color=red!70!black,domain=0:5,samples=2] {1.075};
 \end{axis}
\end{tikzpicture}
\end{document}

enter image description here

0

A solution with pstricks:

\documentclass[11pt,svgnames, border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{fourier}

\usepackage{pst-plot, multido}
\usepackage{auto-pst-pdf}
\def\f{((x^7 + 3*x^6-2*x^5-x^4-3*x^2 + 1)/(x^4-2*x^2))^(1/3)}
\def\g{-((x^7 + 3*x^6-2*x^5-x^4-3*x^2 + 1)/(2*x^2- x^4))^(1/3)}

\begin{document}

\psset{plotstyle=curve, algebraic, arrowinset=0.15, dx=2,Dx = 2}%
\psset{subgriddiv=2,gridcolor=LightSteelBlue, subgridcolor=LightSteelBlue!40, yunit=1.25}
\sffamily
\begin{pspicture}(-0.5,-0.8)(8.5, 6.5)
\psclip{\psframe(-0.5,-0.8)(8.5,6.5)}
\psgrid[xunit=2, yunit=2, gridlabels=0pt, subgriddiv = 4]
\psaxes[labels=none, arrows=->, arrowscale=1.3, xsubticks=4, ysubticks=2, subtickcolor=black](0,0)(7.5,5.8)[$x$,-130] [$y$,-40]%
\uput[r](0,2){2.688}\uput[r](0,4){5.375}\uput{12pt}[l](8.5,2){2.688}\uput{12pt}[l](8.5,4){5.375}
 \psplot[plotpoints=10, linewidth=1.2pt, linecolor=DodgerBlue]{0.549631}{1.103438}{\f}
 \psplot[plotpoints=10, linewidth=1.2pt, linecolor=DodgerBlue]{0.41}{0.54963}{\g}
 \psplot[plotpoints=10, linewidth=1.2pt, linecolor=DodgerBlue]{1.103439}{1.414}{\g}
\psplot[plotpoints=200, linewidth=1.2pt, linecolor=DodgerBlue]{1.418}{8}{\f}
\psline[linecolor=LightSeaGreen](1.4,-1)(1.4,8)
\psline[linecolor=LightSeaGreen](0,0)(8,8)
\multido{\n = -0.5 + 0.5}{16}{\psline[linewidth=0.3pt](\n, -0.8)(\n, -0.65)\psline[linewidth=0.3pt](\n, 6.5)(\n, 6.35)%
 \psline[linewidth=0.3pt](-0.5, \n)(-0.35,\n) \psline[linewidth=0.3pt](8.5, \n)(8.35,\n)}
\multido{\i = 0 + 2}{5}{\uput{10pt}[d](\i, 0){\i}\psline(\i, -0.8)(\i, -0.6)%
\psline(-0.5,\i)(-0.25,\i)\psline(8.5,\i)(8.25,\i)
\uput{11pt}[d](\i, 6.5){\i}\psline(\i, 6.5)(\i,6.3)}
\endpsclip
\end{pspicture}

\end{document}

enter image description here

Bernard
  • 271,350