Plot of which diverges at .
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
xlabel = $z$,
smooth,thick,
axis lines = center,
every tick/.style = {thick},
legend pos=north west]
\addplot[color=blue,domain=0:1.1,samples=150]{-ln(1-x)};
\legend{$-\ln(1 - z)$}
\end{axis}
\end{tikzpicture}
\end{document}