# Graph of polynomial, scaling y-axis

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}

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Welcome to TeX.SE. Thanks for providing a code snippet to show that you made an attempt. But, it is better to compose a fully compilable MWE that illustrates the problem including the \documentclass and the appropriate packages so that those trying to help don't have to recreate it. – Peter Grill Apr 10 '12 at 0:02

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:

## 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}

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With tkz-fct (and gnuplot), it's easy ...

\documentclass{article}
\usepackage{tkz-fct}
\begin{document}
\begin{tikzpicture}
\tkzInit[xmin=-5,xmax=5,ymin=-40,ymax=40,ystep=8]
\tkzGrid
\tkzAxeXY
\tkzFct[color=blue,thick,domain = -5:5]{x**3-3*x};
\end{tikzpicture}
\end{document}


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