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\documentclass[12pt]{article}
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\usepackage{pgf,tikz}
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\usetikzlibrary{arrows}
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\pagestyle{empty}
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\begin{document}
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\definecolor{uuuuuu}{rgb}{0.27,0.27,0.27}
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\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
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\draw[->,color=black] (-1.66,0) -- (9.56,0);
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\draw[->,color=black] (-3.74,0) -- (7.48,0);
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\foreach \x in {-1.57,1.57,π,4.71,6.28,7.85,9.42}
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\foreach \x in {-3,-2,-1,1,2,3,4,5,6,7}
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\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
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\draw[color=black] (9.26,0.08) node [anchor=south west] { x};
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\draw[->,color=black] (0,-3.34) -- (0,5.56);
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\draw[->,color=black] (0,-1.36) -- (0,7.54);
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\foreach \y in {-3,-2,-1,1,2,3,4,5}
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\foreach \y in {-1,1,2,3,4,5,6,7}
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\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};
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\draw[color=black] (0.1,7.12) node [anchor=west] { y};
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\clip(-3.74,-3.34) rectangle (7.48,5.56);
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\draw[smooth,samples=100,domain=0.0:2.0] plot(\x,{cos(((\x)*3.1415926535/2)*180/pi)+3});
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\clip(-1.66,-1.36) rectangle (9.56,7.54);
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\draw[smooth,samples=100,domain=3.0:5.0] plot(\x,{1/((\x)-5)+5});
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\draw plot[raw gnuplot, id=func3] function{set samples 100; set xrange [0.1:1.9]; plot cos((x*3.1415926535/2)*180/pi)+3};
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\draw[smooth,samples=100,domain=2.0:3.0] plot(\x,{0-cos(((\x)*3.1415926535/2)*180/pi)+3});
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\draw plot[raw gnuplot, id=func4] function{set samples 100; set xrange [3.1:4.9]; plot 1/(x-5)+5};
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\draw plot[raw gnuplot, id=func5] function{set samples 100; set xrange [2.1:2.9]; plot -cos((x*3.1415926535/2)*180/pi)+3};
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\draw[color=uuuuuu] (0.14,4.28) node {$A$};
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\fill [color=uuuuuu] (3,3) circle (1.5pt);
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\draw[color=uuuuuu] (3.16,3.28) node {$B$};
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\draw [color=uuuuuu] (2,2) circle (1.5pt);
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\draw[color=uuuuuu] (2.16,2.28) node {$D$};
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\draw [color=uuuuuu] (2,4) circle (1.5pt);
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\draw[color=uuuuuu] (2.16,4.28) node {$E$};
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\draw [color=uuuuuu] (3,4.5) circle (1.5pt);
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\draw[color=uuuuuu] (3.14,4.78) node {$F$};
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\end{scriptsize}
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\end{tikzpicture}
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\end{document}