Multiple Different Curves on a single chart with their own Axis

Question

I'm able to plot a single chart but not certain how multiple charts can be layered with parallel lines connecting them all. An example is below; any help is greatly appreciated.

Answer 1

You may just add several axis object shifted relative to each other.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[/pgfplots/.cd,axis
    lines=left,width=4cm,xtick=\empty,ytick=\empty]
\begin{axis}
 \addplot[mark=none] {exp(-x)};
\end{axis}
\begin{axis}[xshift=-1cm,yshift=-1cm]
 \addplot[mark=none] {exp(-pow(x-2,2))};
\end{axis}
\begin{axis}[xshift=-2cm,yshift=-2cm]
 \addplot[mark=none] {x^2};
\end{axis}
\end{tikzpicture}
\end{document}

If you had data, I could use it and probably use a loop to simplify the code. For now, I use random plots.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}[/pgfplots/.cd,axis
    lines=left,width=4cm,xtick=\empty,ytick=\empty,ymax=2,ymin=-0.5,
    xlabel=$t$]
\foreach \X in {1,...,4}
{\begin{axis}[xshift=-\X*1cm,yshift=-\X*1cm,ylabel=$f_\X(t)$]
  \addplot[mark=none,smooth] {rnd};
  \path (-3,-0.5) coordinate (L\X) (3,-0.5) coordinate (R\X) ;
 \end{axis}}
 \draw[densely dashed] (L1) -- (L4) (R1) -- (R4);
\end{tikzpicture}
\end{document}