document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169709>Question 1169709</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for each of the following, give the amplitude, the period, and describe any vertical or horizontal shifts away from the origin(i.e. from the standard parent graph)\r<BR>\n" );
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document.write( "2a f(x) = -2sin[3(x-pi/2)] + 4\r<BR>\n" );
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document.write( "b. f(x) = -cos(2x -pi/4) -3\r<BR>\n" );
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document.write( "c. f(x) = 2tan(x/3) -1\r<BR>\n" );
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document.write( "d. f(x) = -sec(pi- 5x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794553 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794553\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "a.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2sin%283%28x-pi%2F2%29%29+%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2sin%283%28x-pi%2F2%29%29+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the amplitude: \r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x+%29=A%2Asin%28Bx-C%29%2BD ALIGN=MIDDLE  ALT=\"f%28x+%29=A%2Asin%28Bx-C%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" > the amplitude is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29 ALIGN=MIDDLE  ALT=\"abs%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29=2+ ALIGN=MIDDLE  ALT=\"abs%28A%29=2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=periodicity_of_sin+%28x%29%2Fabs%28B%29 ALIGN=MIDDLE  ALT=\"periodicity_of_sin+%28x%29%2Fabs%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-2sin%28%283x-3pi%2F2%29%29%2B+4 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-2sin%28%283x-3pi%2F2%29%29%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28x%29 ALIGN=MIDDLE  ALT=\"sin%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > periodicity is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=3 ALIGN=MIDDLE  ALT=\"B=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F3 ALIGN=MIDDLE  ALT=\"2pi%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " vertical shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=4 ALIGN=MIDDLE  ALT=\"D=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units up\r<BR>\n" );
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document.write( "horizontal shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FB ALIGN=MIDDLE  ALT=\"C%2FB\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=3pi%2F2 ALIGN=MIDDLE  ALT=\"C=3pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=3 ALIGN=MIDDLE  ALT=\"B=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FB=%283pi%2F2%29%2F3=cross%283%29pi%2F%282%2Across%283%29%29=pi%2F2 ALIGN=MIDDLE  ALT=\"C%2FB=%283pi%2F2%29%2F3=cross%283%29pi%2F%282%2Across%283%29%29=pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29+=+-cos%282x+-pi%2F4%29+-3 ALIGN=MIDDLE  ALT=\"+f%28x%29+=+-cos%282x+-pi%2F4%29+-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the amplitude: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28A%29=1+ ALIGN=MIDDLE  ALT=\"abs%28A%29=1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period:\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28x%29 ALIGN=MIDDLE  ALT=\"cos%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > periodicity is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2 ALIGN=MIDDLE  ALT=\"B=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F2=pi ALIGN=MIDDLE  ALT=\"2pi%2F2=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " vertical shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-3 ALIGN=MIDDLE  ALT=\"D=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > units down\r<BR>\n" );
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document.write( "horizontal shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FB=%28pi%2F4%29%2F2=pi%2F8 ALIGN=MIDDLE  ALT=\"C%2FB=%28pi%2F4%29%2F2=pi%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2tan%28x%2F3%29+-1 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2tan%28x%2F3%29+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+2tan%28%281%2F3%29x%29+-1 ALIGN=MIDDLE  ALT=\"f%28x%29+=+2tan%28%281%2F3%29x%29+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=+1%2F3 ALIGN=MIDDLE  ALT=\"B=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=0 ALIGN=MIDDLE  ALT=\"C=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-1 ALIGN=MIDDLE  ALT=\"D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the amplitude: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none ALIGN=MIDDLE  ALT=\"none\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  doesn’t have amplitude\r<BR>\n" );
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document.write( "the period: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=1%2F3 ALIGN=MIDDLE  ALT=\"B=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28x%29 ALIGN=MIDDLE  ALT=\"tan%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > periodicity is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi ALIGN=MIDDLE  ALT=\"+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F%281%2F3%29=3pi ALIGN=MIDDLE  ALT=\"pi%2F%281%2F3%29=3pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertical shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-1 ALIGN=MIDDLE  ALT=\"D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > units down\r<BR>\n" );
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document.write( "horizontal shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FB=0%2F%281%2F3%29=0 ALIGN=MIDDLE  ALT=\"C%2FB=0%2F%281%2F3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-sec%28pi-+5x%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-sec%28pi-+5x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "amplitude: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none ALIGN=MIDDLE  ALT=\"none\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't have amplitude\r<BR>\n" );
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document.write( "the period: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-5 ALIGN=MIDDLE  ALT=\"B=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28B%29=5 ALIGN=MIDDLE  ALT=\"abs%28B%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%28x%29 ALIGN=MIDDLE  ALT=\"sec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > periodicity is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the period is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2F5 ALIGN=MIDDLE  ALT=\"2pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "vertical shift:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+D=0 ALIGN=MIDDLE  ALT=\"+D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > -> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertical shift\r<BR>\n" );
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document.write( "horizontal shift: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2FB=pi%2F5 ALIGN=MIDDLE  ALT=\"C%2FB=pi%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );