\documentclass[12pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{uuuuuu}{rgb}{0.27,0.27,0.27}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw[->,color=black] (-3.74,0) -- (7.48,0);
\foreach \x in {-3,-2,-1,1,2,3,4,5,6,7}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-3.34) -- (0,5.56);
\foreach \y in {-3,-2,-1,1,2,3,4,5}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
\clip(-3.74,-3.34) rectangle (7.48,5.56);
\draw[smooth,samples=100,domain=0.0:2.0] plot(\x,{cos(((\x)*3.1415926535/2)*180/pi)+3});
\draw[smooth,samples=100,domain=3.0:5.0] plot(\x,{1/((\x)-5)+5});
\draw[smooth,samples=100,domain=2.0:3.0] plot(\x,{0-cos(((\x)*3.1415926535/2)*180/pi)+3});
\begin{scriptsize}
\fill [color=uuuuuu] (0,4) circle (1.5pt);
\draw[color=uuuuuu] (0.14,4.28) node {$A$};
\fill [color=uuuuuu] (3,3) circle (1.5pt);
\draw[color=uuuuuu] (3.16,3.28) node {$B$};
\draw [color=uuuuuu] (2,2) circle (1.5pt);
\draw[color=uuuuuu] (2.16,2.28) node {$D$};
\draw [color=uuuuuu] (2,4) circle (1.5pt);
\draw[color=uuuuuu] (2.16,4.28) node {$E$};
\draw [color=uuuuuu] (3,4.5) circle (1.5pt);
\draw[color=uuuuuu] (3.14,4.78) node {$F$};
\end{scriptsize}
\end{tikzpicture}
\end{document}