Ways of Describing Functions

\documentclass{standalone}
\usepackage{pgfplots} % Plotting library

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        xlabel = $x$,
        ylabel = $f(x)$,
        y = 1cm,
        x = 1cm,
        xmin = 0, xmax = 4, ymin = 0, ymax = 10,
        axis lines = middle,
        xlabel style = {anchor = west, xshift = 5pt},
        ylabel style = {anchor = south, yshift = 5pt}
    ]
    \pgfplotsinvokeforeach{0,...,3}{
        \addplot[domain = 0:4, only marks, blue, very thick] coordinates {(#1, #1^2)};
    }
    \end{axis}
\end{tikzpicture}

\end{document}