[Tex/LaTex] Graph of polynomial, scaling y-axis

tikz-pgf

I'm new to TikZ and to this site, so forgive me if a similar question has already been asked.

I'd like to graph the polynomial function f defined by f(x) = x³ – 6x². I want the y-axis scaled so that the graph of f fits. (I had to manually change the numbers on the y-axis. Such a noob, I know.) If I don't plot the graph of f, I have a nice, centered coordinate system. Adding the function messes up everything. Can someone help me with this? Here is my current setup:

\begin{center}
\begin{tikzpicture}[>=stealth]
%The following places numerals along the x-axis
\coordinate (-5 on x)   at  (0,5);
\node [below left]  at  (-5 on x)   {\small $-5$};
\coordinate (-4 on x)   at  (1,5);
\node [below left]  at  (-4 on x)   {\small $-4$};
\coordinate (-3 on x)   at  (2,5);
\node [below left]  at  (-3 on x)   {\small $-3$};
\coordinate (-2 on x)   at  (3,5);
\node [below left]  at  (-2 on x)   {\small $-2$};
\coordinate (-1 on x)   at  (4,5);
\node [below left]  at  (-1 on x)    {\small $-1$};
\coordinate (0 on x)    at  (5,5);
\node [below left]  at  (0 on x)    {\small $0$};
\coordinate (1 on x)    at  (6,5);
\node [below left]  at  (1 on x)    {\small $1$};
\coordinate (2 on x)    at  (7,5);
\node [below left]  at  (2 on x)    {\small $2$};
\coordinate (3 on x)    at  (8,5);
\node [below left]  at  (3 on x)    {\small $3$};
\coordinate (4 on x)    at  (9,5);
\node [below left]  at  (4 on x)    {\small $4$};
\coordinate (5 on x)    at  (10,5);
\node [below left]  at  (5 on x)    {\small $5$};

%The following places numerals along the y-axis
\coordinate (-40 on y)  at  (5,0);
\node [below left]  at  (-40 on y)  {\small $-40$};
\coordinate (-32 on y)  at  (5,1);
\node [below left]  at  (-32 on y)  {\small $-32$};
\coordinate (-24 on y)  at  (5,2);
\node [below left]  at  (-24 on y)  {\small $-24$};
\coordinate (-16 on y)  at  (5,3);
\node [below left]  at  (-16 on y)  {\small $-16$};
\coordinate (-8 on y)   at  (5,4);
\node [below left]  at  (-8 on y)   {\small $-8$};
\coordinate (8 on y)    at  (5,6);
\node [below left]  at  (8 on y)    {\small $8$};
\coordinate (16 on y)   at  (5,7);
\node [below left]  at  (16 on y)   {\small $16$};
\coordinate (24 on y)   at  (5,8);
\node [below left]  at  (24 on y)   {\small $24$};
\coordinate (32 on y)   at  (5,9);
\node [below left]  at  (32 on y)   {\small $32$};
\coordinate (40 on y)   at  (5,10);
\node [below left]  at  (40 on y)   {\small $40$};
%The following draws the grid lines
\draw[help lines] (-0.25,-0.25) 
  grid (10.25,10.25);
%The following draws the x-axis
\draw[line width=1.0pt,->] (-0.5,5) -- (10.5,5) 
  node[right] {$x$}; 
%The following draws the y-axis
\draw[line width=1.0pt,->] (5,-0.5) -- (5,10.5) 
  node[above] {$y$};
\draw[color=blue,domain=-3:5.2] 
  plot (\x+5,{5+(\x*\x*\x/8)-(3*\x)/8}) 
  node[right] {$f(x) = x^3 - 3x$};
\end{tikzpicture}
\end{center}

Best Answer

Your domain is too large. So setting it to domain=-3:3.8 yields decent results.

However, there are other suggestions:

1. Use `\foreach`

You should use \foreach loops for repetitive tasks. For instance, code identical to yours that places the labels can more easily be written as (with \usetikzlibrary{calc} in the preamble):

    %The following places numerals along the x-axis
    \foreach \x in {-5,...,5}{%
        \coordinate (\x on x)   at  ($(\x,5)+(5,0)$);
        \node [below left]  at  (\x on x)   {\small $\x$};
    }%

    %The following places numerals along the y-axis
    \foreach \y in {-40,-32,...,40}{%
        \coordinate (\y on y)   at  ($(5,\y/8)+(0,5)$);
        \node [below left]  at  (\y on y)   {\small $\y$};
    }%

2. Use `pgfplots` for plotting.

This greatly simplifies these kinds of tasks. Below is a minimal example of your code which produces:

enter image description here

References:

Consistently specify a Function and use it for computation and plotting

Code:

\documentclass{article}
\usepackage{pgfplots}

\def\FunctionF(#1){(#1)^3- 3*(#1)}%

\begin{document}
\begin{tikzpicture}
\begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-5.5,
        xmax=5.5,
        ymin=-45,
        ymax=45,
        height=12.0cm,
        width=12.0cm,
        grid,
        xtick={-5,...,5},
        ytick={-40,-32,...,40},
    ]
    \addplot [domain=-5:5, samples=50, mark=none, ultra thick, blue] {\FunctionF(x)};
    \node [left, blue] at (axis cs: 3.6,42) {$x^3-3x$};
\end{axis}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Drawing Axis Grid in 3D with Custom Unit Vectors

The implementation of canvas is xy plane at z in tikzlibrary3d.code.tex is incorrect, it merely sets a coordinate shift, but doesn't activate the full transformation code necessary. You can redefine the key correctly within your document:

\documentclass{standalone}

\usepackage{xparse}
\usepackage{tikz}

\usetikzlibrary{3d}
\makeatletter
\tikzoption{canvas is xy plane at z}[]{%
  \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}%
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  \tikz@canvas@is@plane
}
\makeatother


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    \def\XGridMax{#3}
    \def\YGridMin{#4}
    \def\YGridMax{#5}
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    \begin{scope}[canvas is yz plane at x=0, thin, blue]
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\NewDocumentCommand{\DrawCoordinateAxis}{O{} m m m m m m}{%
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% A macro to save repeating the code
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\begin{document}
\begin{tikzpicture}[
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    \DrawCoordinateGrid{0}{4}{0}{4}{0}{4}
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\end{tikzpicture}
%
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\end{tikzpicture}
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[Tex/LaTex] Scaling graph along x axis

If you use ytick=data pgfplots puts a tick for each coordinate you insert so your first coordinate overlaps.. in my opinion the better way of showing such data is to use a semilog axis environment in this way:

\documentclass{scrartcl}
\usepackage[no-math]{fontspec}
\usepackage{polyglossia}
\setmainlanguage{brazil}  
\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{semilogyaxis}[ %
bar width=9pt,
nodes near coords,
%y tick label style={/pgf/number format/.cd,fixed,use comma,scaled y ticks=false},
scaled ticks=false,
width=1.0\textwidth,
%height=1.0\textheight,
xlabel={Ano},
ylabel={População},
xmin=0, ymin=0,
xmax=350,
%ytick=data
xtick=data,
]
\addplot coordinates {
(40,1000)
(50,1400)
(100,7530)
(150,40496)
(200,217795)
(250,1171356)
(300,6299832)
(350,33882008)
};
\end{semilogyaxis}
\end{tikzpicture}

\end{document}