# Limit the codomain of a function

I have this code

\begin{tikzpicture}
\def\a{5}
\draw[->] (-\a,0) -- (+\a,0);
\draw[->] (0,-\a) -- (0,+\a);
\draw[thick, red,  samples=100, domain=-.7:3.2] plot ({\x},{ \x*\x*(1-\x)*(3-\x) });
\def\E{2}
\draw[thick, green] (-\a,\E) -- (+\a,\E) node[xshift=0.5cm] {$E$};
\end{tikzpicture}

and I have this output

How to limit the codomain range?

There is a dedicated plotting package built on tikz namely, pgfplots. One implementation of your plot in that could be:

\documentclass{article}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[domain=-.7:3.2, ymin=-1, ymax=1,
axis x line=middle, axis y line=middle, ticks=none,
enlarge x limits={rel=0.07}]
\addplot[green] {(.5)} node[right]{$E$};
\end{axis}
\end{tikzpicture}

\end{document}

You can move the codomain restrictions to just the one function, but putting them as options to the \addplot command, but you have to use the option

restrict y to domain=-1:1

and to get the cut-off right in your example you then have to increase the number of samples:

\documentclass{article}

\usepackage{pgfplots}

\begin{document}

\begin{tikzpicture}
\begin{axis}[domain=-.7:3.2,
axis x line=middle, axis y line=middle, ticks=none,
enlarge x limits={rel=0.07}]
\addplot[thick, red, samples=5000, restrict y to domain=-1:1] {(x*x*(1-x)*(3-x))};
\addplot[green] {(.5)} node[right]{$E$};
\end{axis}
\end{tikzpicture}

\end{document}

If you want to control the axis lengths precisely, use xmin/xmax/ymin/ymax and adjust the domains on the individual plots:

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}

\begin{tikzpicture}
\begin{axis}[xmin=-5, xmax=5, ymin=-1.2, ymax=1.2,
axis x line=middle, axis y line=middle, ticks=none]
domain=-.7:3.2, restrict y to domain=-1:1] {(x*x*(1-x)*(3-x))};
\addplot[domain=-5:4.2, green] {(.5)} node[right]{$E$};
\end{axis}
\end{tikzpicture}

\end{document}
• restrict y to domain=a:b is probably more what the OP wants. – Torbjørn T. Oct 19 '17 at 8:53
• @TorbjørnT. I used that initially, but found it was clipping at the wrong places, perhaps because it requires more samples... – Andrew Swann Oct 19 '17 at 8:56
• True, that can be a problem. – Torbjørn T. Oct 19 '17 at 8:58
• So there is no way to restric only the plot of the function? – Andrea Leo Oct 19 '17 at 9:12
• Yes, just put the options (either restrict y to domain or ymin/ymax) in the \addplot command rather than the axis, if that is what you want. – Andrew Swann Oct 19 '17 at 10:13

\clip? The purpose of the scope environment is to localize the effect of the \clip.

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def\a{5}
\def\E{2}
\draw[->] (-\a,0) -- (+\a,0);
\draw[->] (0,-\a) -- (0,+\a);
\begin{scope}
\clip (-\a,-\a) rectangle (\a,\E);
\draw[thick, red,  samples=100, domain=-.7:3.2] plot ({\x},{ \x*\x*(1-\x)*(3-\x) });
\end{scope}
\draw[thick, green] (-\a,\E) -- (+\a,\E) node[xshift=0.5cm] {$E$};
\end{tikzpicture}
\end{document}
• Thank you but I prefer some solution like \draw[thick, red, samples=100, domain=-.7:3.2, codomain = somerange: somerange] – Andrea Leo Oct 19 '17 at 8:41
• @AndreaLeo pgfplots (see Andrew's answer) and its restrict y to domain key perhaps. I don't know at the moment how to do that, though others might come up with something. – Torbjørn T. Oct 19 '17 at 8:56
• @AndreaLeo You could always wrap the scope, \clip and \draw into one \newcommand, if you must do this in one line of code. – Torbjørn T. Oct 19 '17 at 10:09