Precisa traçar uma função no sistema de coordenadas

Question

Gostaria de traçar uma função racional em LaTeX. Tentei maneiras diferentes com Tikzou pgfplots... nada funciona. Existem muitas maneiras diferentes. Freqüentemente há problemas com pólos/assintotas etc.

\frac{1}{x^2 - 7x - 30}

Estou procurando uma maneira fácil de plotar, mas também gosto do design \usetikzlibrary{datavisualization.formats.functions}que me oferece muitas opções gráficas úteis.

Obrigado

--

Um pouco do meu código:

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{tikz,pgfplots}
\usetikzlibrary{datavisualization.formats.functions}

\begin{document}
\begin{tikzpicture}[yscale=.5, xscale=.5, scale=2]
\datavisualization
[school book axes,
legend={below,rows=1},
visualize as smooth line/.list={f1},
f1={style=blue, style=very thick,label in legend={text=$\frac{1}{x-1}$}},
%f2={style=green, style=very thick,label in legend={text=$\frac{1}{x^2 - 7x - 30}$}}
]
data [set=f1, format=function] {
var x : interval[-4:0.5];
func y = 1/(\value{x} - 1);
}data [set=f1, format=function] {
var x : interval[1.5:4];
func y = 1/(\value x - 1);
};
data [set=f2, format=function] {
var x : interval[12:20];
func y = 1/(\value{x}^2 - 7 \value{x} - 30);
};
\end{tikzpicture}   
\end{document}

Isto resulta em

Próximo passo, agora tenho:

\begin{tikzpicture}[scale=1.5]
  \begin{axis}[axis lines=middle,xmin=-20,xmax=20,ymin=-1.5,ymax=1.5,
    extra x ticks={-2,2},
    xlabel=$\scriptstyle x$,
    ylabel=$\scriptstyle y$,
    tick label style={font=\tiny},
    legend style={font=\small,legend pos=outer north east,}]
    \addplot+[no marks,blue,domain=-15:0.8,samples=150, thick] {1/(x - 1)};
        \addplot+[no marks,blue,domain=1.2:15,samples=150, thick] {1/(x - 1)};
    \addlegendentry{$\frac{1}{x-1}$}
    \addplot+[no marks,red,domain=-15:-3.02,samples=150, thick] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,red,domain=-2.98:9.98,samples=150, thick] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,red,domain=10.02:15,samples=150, thick] {1/((x)^2 - 7*x-30)};
    \addlegendentry{$\frac{1}{x^2 - 7x - 30}$}
  \end{axis}
\end{tikzpicture}

Como posso adicionar mais números entre o intervalo do eixo xmin/xmax? Por exemplo, escreva a cada 2 números inteiros?

Answer 1

Compgfplots

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[axis lines=middle,xmin=-7,xmax=17,ymin=-1.5,ymax=1.5,xlabel=$\scriptstyle x$,ylabel=$\scriptstyle y$,tick label style={font=\tiny},legend style={font=\tiny,legend pos=outer north east,}]
    \addplot+[no marks,domain=-10:0.5,samples=150] {1/(x - 1)};
    \addlegendentry{$\frac{1}{x-1}$}
    \addplot+[no marks,olive,domain=-7:-3.02,samples=150] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,olive,domain=-2.98:9.98,samples=150] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,olive,domain=10.02:15,samples=150] {1/((x)^2 - 7*x-30)};
    \addlegendentry{$\frac{1}{x^2 - 7x - 30}$}
  \end{axis}
\end{tikzpicture}
\end{document}

Com restrict y to domain=-10:10,, você consegue isso:

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[axis lines=middle,xmin=-7,xmax=17,ymin=-1.5,ymax=1.5,xlabel=$\scriptstyle x$,ylabel=$\scriptstyle y$,tick label style={font=\tiny},legend style={font=\tiny,legend pos=outer north east,},restrict y to domain=-10:10,]
    \addplot+[no marks,domain=-10:0.5,samples=150] {1/(x - 1)};
    \addlegendentry{$\frac{1}{x-1}$}
    \addplot+[no marks,olive,domain=-7:15,samples=150] {1/((x)^2 - 7*x-30)};
    \addlegendentry{$\frac{1}{x^2 - 7x - 30}$}
  \end{axis}
\end{tikzpicture}
\end{document}

Para situações críticas, você também pode precisar unbounded coords=jump,logo depois restrict y to domain=-10:10,.

Para a edição, você pode fazer isso:

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[axis lines=middle,
    xmin=-8,xmax=18,
    ymin=-1.6,ymax=1.6,
    xtick={-6,-4,...,16},
    ytick={-1.4,-1.2,...,1.4},
    xlabel=$\scriptstyle x$,
    ylabel=$\scriptstyle y$,
    tick label style={font=\tiny},
    legend style={font=\tiny,legend pos=outer north east,}
    ]
    \addplot+[no marks,line width=1pt,domain=-10:0.5,samples=150] {1/(x - 1)};
    \addlegendentry{$\frac{1}{x-1}$}
    \addplot+[no marks,line width=1pt,olive,domain=-7:-3.02,samples=150] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,line width=1pt,olive,domain=-2.98:9.98,samples=150] {1/((x)^2 - 7*x-30)};
    \addplot+[no marks,line width=1pt,olive,domain=10.02:15,samples=150] {1/((x)^2 - 7*x-30)};
    \addlegendentry{$\frac{1}{x^2 - 7x - 30}$}
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

Caso você esteja interessado, também é fácil com pst-plot:

\documentclass[12pt, svgnames,x11names, pdf]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{nccmath}
\usepackage{lmodern}

\usepackage{pst-plot}

\begin{document}

 \def\F{1/(x^2-7*x-30)}
\def\G{1/(x-1)}
 \footnotesize\everymath{\scriptstyle}
\psset{xunit=0.6, yunit=3, linewidth=0.6pt, ticksize=-2pt 2pt, labels=y, Dx=5, arrowinset=0.2}
\begin{pspicture*}(-7,-1.25)(15,1.6)
\psaxes[arrows=->](0,0)(-7,-1.25)(15,1.6)[ $ x $, -135][ $ y $,-135]%
\uput[-120](0,0){$ 0 $}% asymptotes
\psline(10,-1.25)(10,1.6)\uput[dr](10,0){$10$}
\psline(-3,-1.25)(-3,1.6)\uput[dl](-3,0){$-3$}
\psline(1,-1.25)(1,1.6)\uput[dr](1,0){$1$}
\psset{linewidth=1pt, linecolor =IndianRed ,plotpoints=100,plotstyle=curve, algebraic, labelsep = 0.5em}
\psplot{-7}{-3.02}{\F}
\psplot{-2.98}{9.98}{\F}
\psplot{10.02}{14.75}{\F}
\psset{linecolor=LightSkyBlue4!80!}
\psplot{-7}{0.98}{\G}
\psplot{14.75}{1.02}{\G}
\end{pspicture*}

\end{document}