document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198583>Question 1198583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is done to the function  g(x)=sin(x) to create the function h(x)=3sin(x-pi/4)\r<BR>\n" );
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document.write( "One of the following is the correct answer. Which one?\r<BR>\n" );
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document.write( "A) the function g(x) is vertically stretched by a factor of 3. It will also be  shifted to the right pi/4 units. \r<BR>\n" );
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document.write( "B) the function g(x) is vertically compressed by a factor of 3. It will also be  shifted to the right pi/4 units. \r<BR>\n" );
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document.write( "C) the function g(x) is vertically compressed by a factor of 3. It will also be  shifted to the left pi/4 units. \r<BR>\n" );
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document.write( "D) the function g(x) is vertically stretched by a factor of 3. It will also be  shifted to the left pi/4 units. \r<BR>\n" );
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document.write( "E) the function g(x) is vertically compressed by a factor of pi/4. It will also be  shifted to the right 3 units.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832187 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=832187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=3sin%28x-pi%2F4%29 ALIGN=MIDDLE  ALT=\"h%28x%29=3sin%28x-pi%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We first need to understand how do the parameters <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=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+ ALIGN=MIDDLE  ALT=\"c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >affect the graph of <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28x%29=a+sin%28bx%2Bc%29+ ALIGN=MIDDLE  ALT=\"f+%28x%29=a+sin%28bx%2Bc%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when compared to the graph of <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;\" >\r<BR>\n" );
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document.write( "a=amplitude: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "period:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi ALIGN=MIDDLE  ALT=\"2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > (periodicity of <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;\" > function)<BR>\n" );
document.write( "phase shift:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%2Fb=%28pi%2F4%29%2F1=pi%2F4 ALIGN=MIDDLE  ALT=\"c%2Fb=%28pi%2F4%29%2F1=pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >---- shifted  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > units to the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=right ALIGN=MIDDLE  ALT=\"right\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " vertical shift: <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( "answer:<BR>\n" );
document.write( "A) the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is vertically stretched by a factor of 3}}}. It will also be shifted to the right <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F4+ ALIGN=MIDDLE  ALT=\"pi%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >units.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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