\begin{tikzpicture}
\begin{axis}[
    title={Figure 5},
    xlabel={$\log_R r$},
    ylabel={$\log_R N_X (r)$},
    xmin=0, xmax=1,
    ymin=0, ymax=1,
    axis lines=left,
    height=5cm,
    ylabel style={rotate=-90,xshift=-0.75cm},
]
\addplot[
    domain=0:1,
    samples=100,
    color=myblue,
]
{x} node[pos=0.5, anchor=south, yshift=5pt, circle, draw=myblue, inner sep=1pt, text=black, fill=white] {\normalfont A};

\addplot[
    domain=0:1,
    samples=100,
    color=mygreen,
]
{max(0, 2*x - 1)} node[pos=0.75, anchor=north, yshift=-16pt, circle, draw=mygreen, inner sep=1pt, text=black, fill=white] {\normalfont B};

\addplot[
    domain=0:1,
    samples=100,
    color=myred,
]
{min(2*x, 1)} node[pos=0.25, anchor=south, yshift=16pt, circle, draw=myred, inner sep=1pt, text=black, fill=white] {\normalfont C};

\end{axis}
\end{tikzpicture}