Piecewise Function in tikzpicture

Question

I'm trying to create a piecewise plot in tikzpicture. Trying to emulate the example from this answer Plotting a piecewise function didn't work for me, and I don't understand why this code isn't working.

\documentclass[11pt, letterpaper]{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[
  declare function={
            func(\x)= (\x<=0) * ((0.5)*exp(\x))   +
            and(\x>0) * (1-(0.5)*exp(-\x))
            ;
        }
        ]
        \begin{axis}[
        axis x line=middle, axis y line=middle,
        ymin=0, ymax=1, ytick={0,0.5,1}, ylabel=$F_{X-Y}(t)$,
        xmin=-5, xmax=5, xtick={-5,...,5}, xlabel=$t$,
        ]
        \addplot[blue, domain=-5:5, smooth]{func(x)};
\end{axis}
\end{tikzpicture} 
\end{document}

Any help would be greatly appreciated!

Answer 1

Welcome! You call and with only one argument, and it seems to me (but I may be wrong) that you do not want an and at all. (You may also change the function to only use abs and sign functions, see the afunc definition.)

\documentclass[11pt, letterpaper]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[
  declare function={
            func(\x)= (\x<=0) * ((0.5)*exp(\x))   +
            (\x>0) * (1-(0.5)*exp(-\x));
            afunc(\x)=0.5*(1+sign(\x)-sign(\x)*exp(-abs(\x)));
        }
        ]
        \begin{axis}[
        axis x line=middle, axis y line=middle,
        ymin=0, ymax=1, ytick={0,0.5,1}, ylabel=$F_{X-Y}(t)$,
        xmin=-5, xmax=5, xtick={-5,...,5}, xlabel=$t$,
        ]
        \addplot[blue, domain=-5:5, smooth]{func(x)};
        \addplot[red, domain=-5:5, smooth,dashed,thick]{afunc(x)};
\end{axis}
\end{tikzpicture} 
\end{document}

Of course, the function may be approximated by a tanh.

\documentclass[11pt, letterpaper]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[
  declare function={
            func(\x)= (\x<=0) * ((0.5)*exp(\x))   +
            (\x>0) * (1-(0.5)*exp(-\x));
        }
        ]
        \begin{axis}[
        axis x line=middle, axis y line=middle,
        ymin=0, ymax=1, ytick={0,0.5,1}, ylabel=$F_{X-Y}(t)$,
        xmin=-5, xmax=5, xtick={-5,...,5}, xlabel=$t$,
        ]
        \addplot[blue, domain=-5:5, smooth]{func(x)};
        \addplot[red, domain=-5:5, smooth,dashed,thick]{0.5*tanh(x/1.5)+0.5};
\end{axis}
\end{tikzpicture} 
\end{document}