Recommended way to draw sets in Euclidean plane

I was wondering which is the most appropriate tool to draw sets in the Euclidean plane (with axis) such as the plane minus a given ray or the points in the plane which have a y coordinate between 2 and 3 . I was about to use pgf plots but that doesn't allow me to shade so freely the given regions (specially in the case of the whole plane minus a couple of points or lines), then I read about tkz-euclide but I have no clue how to use that one. Any suggestion?

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Here's an example using pgfplots to draw some of the regions mentioned (the region bounded by two horizontal straight lines, the region outside a horizontal strip, the plane minus some rays, the plane minus some points):

\documentclass[border=3pt,varwidth=true,varwidth=40cm]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
ymin=-1,
ymax=4
]
\end{axis}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
ymin=-3,
ymax=3
]
\end{axis}
\end{tikzpicture}\par\bigskip
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
ymin=-3,
ymax=3
]
\draw[fill=white]
\draw[double,double distance=2pt]
([shift={(0:2.7pt)}]axis cs:0,0) -- ++(0:30cm);
\draw[double,double distance=2pt]
([shift={(135:2.7pt)}]axis cs:0,0) -- ++(135:30cm);
\end{axis}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
ymin=-3,
ymax=3
]