\documentclass[margin=0.5cm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18} 

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
    title={Logit function},
    xlabel={$x$},
    ylabel={$y$},
    domain=-5:5,
    samples=200,
    legend style={at={(0.95,0.05)},anchor=south east}
]
\newcommand{\Lvar}{1}
\newcommand{\kvar}{1}
\newcommand{\xvar}{0}
\addplot [blue] {\Lvar / (1 + exp(-\kvar*(x-\xvar)))};
\addlegendentry{$L = \Lvar, k=\kvar, x_0=\xvar$};
\end{axis}
\end{tikzpicture}
\end{document}