Coordinate system confusion of TikZ and PGFPlots

Question

So, I'm drawing graphs using TikZ and pgfplots for my lecture notes. My question is about the two coordinate systems that are used in the following code:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[axis lines = center, xlabel = $x$, ylabel =$y$, ymax=3, ymin=-1, xmax=5, xmin=-1 ,samples=500, ytick={1,2}, xtick={1,2,3,4}]
% Code for the graph.
\addplot[blue, domain=2.05:4.5, thick] {-x + 4};
\addplot[blue, domain=-0.5:1.95, thick] {x};
\draw[blue] (300,297) circle[radius=1.5pt];
\node[above right] at (300,297) {\footnotesize $y=f(x)$};
\end{axis}
\end{tikzpicture}
\end{document}

Question: Why is it that the lines of the graph can be drawn with the coordinates of the axes, but the coordinates of the nodes have to be specified using some other system?

Question: What is the other system? Is it easy to say where (0,0) in the "node system" is with respect to (0,0) on the axes?

Ideally I would like to be able to use the axes coordinates for all aspects of the diagram. But, any help at all would be great!

Thanks in advance.

Answer 1

As Torbjørn T. already mentioned in the comment below the question you can use the axis coordinate system also for TikZ stuff by adding \pgfplotsset{compat=1.11} to the preamble.

To (hopefully) answer the remaining questions please have a look at the following code and its comments.

More details can be found in the PGFPlots manual (v1.17). Have a look at

• section 4.17.1 "Accessing Axis Coordinates in Graphical Elements" and
• section 4.19.1 "Basic Alignment".

% used PGFPlots v1.17
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % use this `compat` level or higher to use `axis cs:` as default
        % coordinate system for TikZ stuff as well.
        compat=1.11,
    }
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        % where to place the `axis` node in the TikZ coordinate system
        % (the default coordinate is (0,0)) ...
        at={(5mm,5mm)},
        % ... with the `anchor`
        % (the default is `south west`)
        anchor=outer south east,
        name=plot,
        % ---------------------------------------------------------------------
        xlabel=$x$,
        ylabel=$y$,
        legend pos=outer north east,
    ]
        \addplot {x^2};
        \legend{$x^2$}
    \end{axis}
% show the origin of the TikZ coordinate system
\fill [red,radius=2pt]   (0,0) circle;
% show the place where the `axis` node was placed
\draw [green,radius=4pt] (plot.outer south east) circle;
% "prove" that the `axis` node is really placed at the given coordinate
\draw [blue] (0,0) -- +(5mm,5mm);

\end{tikzpicture}
\end{document}