\documentclass{scrartcl}
\usepackage{color}
\usepackage{multicol}
\usepackage[final]{graphicx}
\usepackage{pst-plot,pstricks}
	\input{pstplot-logarithmic-axes}
\begin{document}
	\psset{xunit=2cm,yunit=2cm}
	\begin{pspicture}(-0.5,-1.5)(5.5,1.5)
		\psgrid[xunit=1,yunit=1,subgriddiv=2,griddots=5,gridlabels=0](0,-1)(5,1)
		\psaxes[Dx=1,Dy=0.5]{->}(0,0)(-0.5,-1.2)(5.5,1.2)
		\psplot{0}{5}{2.71828 x -2 div exp}
		\psplot[linestyle=dashed]{0}{2}{1 x 0.5 mul sub}
		\psplot{0}{5}{2.71828 x -1 div exp -1 mul}
		\psplot[linestyle=dashed]{0}{1}{x 1 sub}
		\psplot[linecolor=red]{1}{5}{2.71828 x -1 add -2 div exp}
		\psplot[linecolor=red,linestyle=dashed]{1}{3}{1.5 x 0.5 mul sub}
		\psplot[linecolor=red]{1}{5}{2.71828 x -1 add -1 div exp -1 mul}
		\psplot[linecolor=red,linestyle=dashed]{1}{2}{x 2 sub}
		\psline[linecolor=red,linestyle=dashed](1,-1)(1,1)
		\psplot[linecolor=green]{0}{5}{1 x 1 add div x 3.1415 div 360 mul sin mul}
	\end{pspicture}
\end{document}
