document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=947646>Question 947646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What would 5 characteristics of this sinusoidal graph be? \r<BR>\n" );
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document.write( "y = 5 sin [3(x-2)] - 1 \r<BR>\n" );
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document.write( "This is what I've figured out; but I want to be sure that I am correct.\r<BR>\n" );
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document.write( "Midline is at y=1<BR>\n" );
document.write( "Amplitude=5<BR>\n" );
document.write( "Maximum=1+5=6<BR>\n" );
document.write( "Minimum=1-5=(-4)<BR>\n" );
document.write( "And the period I have no idea what it is. \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578297 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=578297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sinusoid is the name given to any curve that can be written in the form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=Asin%28B%28x-C%29%29%2BD ALIGN=MIDDLE  ALT=\"y=Asin%28B%28x-C%29%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ................(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > are positive). \r<BR>\n" );
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document.write( "|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >| = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=amplitude ALIGN=MIDDLE  ALT=\"amplitude\"   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 ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" > = cycles from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=period+=2pi%2FB ALIGN=MIDDLE  ALT=\"period+=2pi%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=D+ ALIGN=MIDDLE  ALT=\"D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= vertical shift (or displacement)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+ ALIGN=MIDDLE  ALT=\"C+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= horizontal shift (sometimes called \"phase shift\" when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+1 ALIGN=MIDDLE  ALT=\"B+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "you have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5+sin+%283%28x-2%29%29-+1+ ALIGN=MIDDLE  ALT=\"y+=+5+sin+%283%28x-2%29%29-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,<BR>\n" );
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document.write( "|<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >| = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (amplitude)\r<BR>\n" );
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document.write( "<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;\" >     (cycles from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=period+=2pi%2FB=2pi%2F3 ALIGN=MIDDLE  ALT=\"period+=2pi%2FB=2pi%2F3\"   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=D+=-1 ALIGN=MIDDLE  ALT=\"D+=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > vertical shift (or displacement <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > unit <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=down ALIGN=MIDDLE  ALT=\"down\"   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+=2 ALIGN=MIDDLE  ALT=\"C+=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ( horizontal shift, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=left ALIGN=MIDDLE  ALT=\"left\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "max<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5+sin%283+%28x-2%29%29-1 ALIGN=MIDDLE  ALT=\"y+=+5+sin%283+%28x-2%29%29-1\"   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;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Bpi%2F6%2B%282n%2Api%29%2F3 ALIGN=MIDDLE  ALT=\"x+=+2%2Bpi%2F6%2B%282n%2Api%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "min{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5+sin%283+%28x-2%29%29-1 ALIGN=MIDDLE  ALT=\"y+=+5+sin%283+%28x-2%29%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >} =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-6 ALIGN=MIDDLE  ALT=\"+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2%2Bpi%2F2%2B%282n%2Api%29%2F3 ALIGN=MIDDLE  ALT=\"x+=+2%2Bpi%2F2%2B%282n%2Api%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for integer <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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