\documentclass[varwidth=false, border=2pt]{standalone}

\usepackage{pgfplots}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
    \begin{axis}[
    	legend pos=north west,
        axis x line=middle,
        axis y line=middle,
        grid = major,
        width=16cm,
        height=8cm,
        grid style={dashed, gray!30},
        xmin=-1,     % start the diagram at this x-coordinate
        xmax= 1,    % end   the diagram at this x-coordinate
        ymin= 0,     % start the diagram at this y-coordinate
        ymax= 1,   % end   the diagram at this y-coordinate
        %axis background/.style={fill=white},
        xlabel=x,
        ylabel=y,
        tick align=outside,
        enlargelimits=false]
      % plot the stirling-formulae
      \addplot[domain=-1:1, red, ultra thick,samples=500] {1/(1+exp(-5*x))};
      \addplot[domain=-1:1, blue, ultra thick,samples=500] {1/(1+exp(-10*x))};
      \addlegendentry{$f(x)=\frac{1}{1+e^{-5x}}$}
      \addlegendentry{$g(x)=\frac{1}{1+e^{-10x}}$}
    \end{axis}
\end{tikzpicture}
\end{document}
