Piecewise defined function in tikz or tkz-fct

Question

How to define and plot a piecewise defined function in tikz or tkz-fct? For example consider the function

f(x) = 1 for x < 0, x for 0 <= x < 1, cos(x) for x >= 1

Edit:

After Torbjørn T.'s comment I tried the following. I should mention that I included three different versions of plotting the function because I want that all three versions should work.

\documentclass{article}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{tkz-fct}

\pgfmathdeclarefunction{p}{3}{%
  \pgfmathparse{(and(#1>#2, #1<#3))}%
}

\pgfmathdeclarefunction{f}{1}{%
  \pgfmathparse{p(#1,-100,0)*1 + p(#1,0,1)*#1 + p(#1,1,100)*cos(#1r)}
}

\begin{document}

\begin{tikzpicture}
   \tkzInit[xmin=-1,xmax=5,ymax=4] %
   \tkzGrid %
   \tkzAxeXY %
   \tkzFct{f(x)} %
   \draw plot function{f(x)};%
      \begin{scope}[xshift=4cm]
      \begin{axis}
         \addplot[domain=-2:4,samples=100]{f(x)};
      \end{axis}
   \end{scope}
\end{tikzpicture}


\end{document}

Which gives the following output:

Answer 1

There are a few problems with the code:

1. PGF uses degrees for trig functions
2. Seems that the r at the end of the function f was intended to convert from radians to degree, but I changed it so that it is more obvious.
3. Need to determine what happens at the end points of the piecewise domain, so note the slight tweaks for that.
4. Not sure what the tkz portion of the code has to do with the problem of defining a piecewise function, so have commented that out.
5. Be careful using single letter function names as documented in: Why do 2 identical function definitions with different names produce two different plots?

So, with slight modifications to your code I can produce the following. Note that there still is a problem around x=1 as pgf does not know what to do.

\documentclass[border=2pt]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{tkz-fct}

\pgfmathdeclarefunction{p}{3}{%
  \pgfmathparse{(and(#1>#2, #1<#3))}%
}

\pgfmathdeclarefunction{f}{1}{%
  \pgfmathparse{p(#1,-100,-0.001)*1 + p(#1,0,1)*#1 + p(#1,1.01,100)*cos(deg(#1))}%
}

\begin{document}
\begin{tikzpicture}
%   \tkzInit[xmin=-1,xmax=5,ymax=4] %
%   \tkzGrid %
%   \tkzAxeXY %
%   \tkzFct{f(x)} %
%   \draw plot function{f(x)};%
      \begin{scope}[xshift=6cm]
      \begin{axis}
         \addplot[ultra thick, blue,domain=-2:4,samples=100]{f(x)};
      \end{axis}
   \end{scope}
\end{tikzpicture}
\end{document}

---

What I would recommend is that you draw the three separate portions individually and avoid the problem areas via a fixed value of \Tolerance:

\documentclass[border=2pt]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\usepackage{tkz-fct}

\pgfmathdeclarefunction{p}{3}{%
  \pgfmathparse{(and(#1>#2, #1<#3))}%
}

\newcommand{\Tolerance}{0.0001}%
\pgfmathdeclarefunction{f}{1}{%
  \pgfmathparse{%
    p(#1,-\maxdimen,-\Tolerance)*1.0 +%
    p(#1,0,1-\Tolerance)*#1 +%
    p(#1,1,\maxdimen)*cos(deg(#1))}%
}

\begin{document}
\begin{tikzpicture}
%   \tkzInit[xmin=-1,xmax=5,ymax=4] %
%   \tkzGrid %
%   \tkzAxeXY %
%   \tkzFct{f(x)} %
%   \draw plot function{f(x)};%
      \begin{scope}[xshift=6cm]
      \begin{axis}
         \addplot[ultra thick, blue,domain=-2:-\Tolerance,samples=100]{f(x)};
         \addplot[ultra thick, green,domain=\Tolerance:1-\Tolerance,samples=100]{f(x)};
         \addplot[ultra thick, red,domain=1+\Tolerance:4,samples=100]{f(x)};
      \end{axis}
   \end{scope}
\end{tikzpicture}
\end{document}

To clarify, the \addplot calls above are really just:

\addplot[ultra thick, blue, domain=-2.0000:-0.0001, samples=100]{f(x)};
\addplot[ultra thick, green,domain= 0.0001: 0.9999, samples=100]{f(x)};
\addplot[ultra thick, red,  domain= 1.0001: 4.0000, samples=100]{f(x)};

Answer 2

I would use the ifthenelse structure (available in tikz and in gnuplot).

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}

% plain tikz + ifthenelse:
\begin{tikzpicture}[scale=3]
  \draw[blue,thick] plot[samples=200,domain=-2:4] (\x,{ifthenelse(\x <
    0,1,ifthenelse(and(\x >= 0,\x < 1),\x, cos(deg(\x))))});  
  \draw[red,thick,semitransparent] plot[samples=200,domain=-2:4]
    (\x,{cos(deg(\x))});   
\end{tikzpicture}

% pgfplots + gnuplot:
\begin{tikzpicture}
  \begin{axis}
    \addplot+[samples=150,domain=-2:4] function {x < 0 ? 1 : ((x >=0)
      && (x<1)) ? x : cos(x)}; 
    \addplot+[samples=150,domain=-2:4,semitransparent] function {cos(x)}; 
  \end{axis}
\end{tikzpicture}

% plain tikz with '?' operator: 
\begin{tikzpicture}[scale=3]
  \draw plot[samples=200,domain=-2:4] (\x,{\x < 0 ? 1 : (((\x >=0)
      && (\x<1)) ? \x : cos(deg(\x)))});
\end{tikzpicture}

% pgfplots without gnuplot: (requires developer version of pgf or pgfplots):
\begin{tikzpicture}
  \begin{axis}
    \addplot[blue,samples=150,domain=-2:4] {x < 0 ? 1 : (((x >=0)
      && (x<1)) ? x : cos(deg(x)))}; 
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 3

Run with xelatex

%f(x) = 1 for x < 0, x for 0 <= x < 1, cos(x) for x >= 1

\documentclass{article}
\usepackage{pstricks-add}
\pagestyle{empty}
\begin{document}    
\begin{pspicture}(-1,-1)(7,1)
\psaxes[trigLabels,xunit=\pstRadUnit,trigLabelBase=3]{->}(0,0)(-1,-1)(7,1.2)
\psplot[algebraic,linecolor=red,plotpoints=1000,
        linewidth=1pt]{-1}{7}{IfTE(x<0,1,IfTE(x<1,x,cos(x)))}
\end{pspicture}
\end{document}

Answer 4

I slightly modified @Herbert's code to make the graph of f (visually) "a graph of a function". It still has few quirks.

\documentclass{article}
\usepackage{pstricks-add}
\pagestyle{empty}
\begin{document}    
\begin{pspicture}(-1,-1)(7,1)
\psplot[algebraic,linecolor=red,plotpoints=1000,
        linewidth=1pt]{-1}{7}{IfTE(x<0,1,IfTE(x<1,x,cos(x)))}
\psline[linecolor=white,linewidth=1pt](0,1)(0,0)
\psline[linecolor=white,linewidth=2pt](1,.96)(1,0.54)
\psaxes[trigLabels,xunit=\pstRadUnit,trigLabelBase=3]{->}(0,0)(-1,-1)(7,1.2)
\end{pspicture}
\end{document}