% Code for the left graph:
\documentclass{standalone}
\usepackage{pgfplots} % Plotting library

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        xlabel = $x$,
        ylabel = $f(x)\ {=}\ 2x+3$,
        y = 1cm,
        x = 1cm,
        xmin = -5, xmax = 5, ymin = -2, ymax = 5,
        axis lines = middle,
        xlabel style = {anchor = west, xshift = 5pt},
        ylabel style = {anchor = south, yshift = 5pt}
    ]
    
    \addplot [blue, very thick, samples = 200] {2*x + 3};
    
    % Add a bunch of colorful horizontal lines. Notice how each horizontal line intersects only ONCE with the blue curve of f(x) = 2x + 3:
    \pgfplotsinvokeforeach{0,...,8}{
        \addplot +[mark = none, very thick] {#1*0.5 + 0.5};
    }
    \end{axis}
\end{tikzpicture}

\end{document}

% Code for the right graph:
\documentclass{standalone}
\usepackage{pgfplots} % Plotting library
\usetikzlibrary{intersections}

\begin{document}

\begin{tikzpicture}
    \begin{axis}[
        xlabel = $x$,
        ylabel = $f(x)\ {=}\ x^2$,
        y = 1cm,
        x = 1cm,
        xmin = -5, xmax = 5, ymin = -2, ymax = 5,
        axis lines = middle,
        xlabel style = {anchor = west, xshift = 5pt},
        ylabel style = {anchor = south, yshift = 5pt}
    ]
    
    \addplot [blue, very thick, samples = 200, name path global = Square] {x^2};
    
    % Add a red horizontal line at y = 2. Notice that this line intersects TWICE with the blue curve: once at a value of x between -2 and -1 (approx -1.414), and another time at a value of x between 1 and 2 (approx +1.414).
    \addplot [mark = none, very thick, red, name path global = Line] {2};
    
    % Mark intersections:
    \fill [name intersections = {of = Square and Line, name = i, total = \t}, red, opacity = 1] 
    \foreach \s in {1,...,\t}{
        (i-\s) circle (3pt)
    };
    
    \end{axis}
\end{tikzpicture}

\end{document}