Plotting a piecewise function

Question

I'm trying to learn to plot in latex, but I'm having a problem trying to find out which packages that are best to use in this situation, and I find it a bit of a learning curve.

Suppose you have the following function:

I would like to know, how I could graph this in Latex. I have searched around and found out that you could use the PGF and tikz packages, and use the declare function, but I have problems with the intervals in which $x$ is defined

How would I approach this problem, as a complete newbie to graphing in Latex? I tried using a similiar post about it, and tried to plug in my intervals. My code looks like this:

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.8}
\begin{document}
\begin{tikzpicture}[
  declare function={
    func(\x)= (\x \in [-\pi, -\frac{pi}{2}) * (0)   +
     and(\x \in [-\frac{\pi}{2},\frac{\pi}{2}) * (\frac{\pi}{2}-|x|)     +
     and(\x \in [\frac{\pi}{2}, \pi]) * (0)
   ;
  }
]
\begin{axis}[
  axis x line=middle, axis y line=middle,
  ymin=-5, ymax=5, ytick={-5,...,5}, ylabel=$y$,
  xmin=-5, xmax=5, xtick={-5,...,5}, xlabel=$x$,
]
\end{axis}
\end{tikzpicture} 
\end{document}

Hi. I found a similiar post, and tried to just plug in the intervals, but it doesn't seem to work. — Hatze, Jun 06 '17 at 08:39
Related: https://tex.stackexchange.com/questions/261533/plotting-piecewise-function-using-declare-function?rq=1, https://tex.stackexchange.com/q/327221/1952 — Ignasi, Jun 06 '17 at 08:40
Which post? Please add the code you have so far to your question. — Torbjørn T., Jun 06 '17 at 08:40
@Hatze to plot the function write \addplot[<your-options>]{func(x)}; inside the axis environment. — marsupilam, Jun 06 '17 at 08:56

Torbjørn T. · Accepted Answer · 2018-11-11T20:46:00.250

11

There are a couple of things you've gotten wrong. First of all, as marsupilam says in a comment, you have to plot the function as well, not just declare it.

Second, you can't use \frac, \pi etc. when declaring functions. They are macros intended for typesetting math, to do a calculation write it like e.g. pi/2.

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
%\pgfplotsset{compat=1.8}
\begin{document}
\begin{tikzpicture}[
  declare function={
    func(\x)= (\x < -pi/2) * (0)   +
              and(\x >= -pi/2, \x < pi/2) * (pi/2-abs(\x))     +
              (\x >= pi/2) * (0)
   ;
  }
]
\begin{axis}[
  axis x line=middle, axis y line=middle,
  ymin=-5, ymax=5, ytick={-5,...,5}, ylabel=$y$,
  xmin=-5, xmax=5, xtick={-5,...,5}, xlabel=$x$,
  domain=-pi:pi,samples=101, % added
]

\addplot [blue,thick] {func(x)};
\end{axis}
\end{tikzpicture} 
\end{document}

edited Nov 11 '18 at 20:46

answered Jun 06 '17 at 09:02

Torbjørn T.

206,688

Do ask if anything is unclear. – Torbjørn T. Jun 06 '17 at 09:02
That makes sense, and I understand the logic behind the syntax. Just one last question; If I wanted more of the function to be drawn, how would I specify that? – Hatze Jun 06 '17 at 09:11
@Hatze The domain setting defines the domain over which to plot the function, if that is what you meant. – Torbjørn T. Jun 06 '17 at 09:13
Okay, I understand. I thank you very much for your help! – Hatze Jun 06 '17 at 09:18
x >= -pi/2 should be replaced by \x >= -pi/2 – Black Mild Nov 11 '18 at 03:58
What about not equal to, in the func setup? – Himanshu Aug 28 '23 at 23:28
@Himanshu !=, as described in chapter 94.2 of the manual (unofficial HTML-version of that at https://tikz.dev/math-parsing#sec-94.2) – Torbjørn T. Aug 29 '23 at 16:44

Plotting a piecewise function

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