document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062627>Question 1062627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Describe the changes in the graph corresponding to changes in a,b,c,d.<BR>\n" );
document.write( "Function: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+d+%2B+a+ ALIGN=MIDDLE  ALT=\"+y+=+d+%2B+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" >sin (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+bx+-+c+ ALIGN=MIDDLE  ALT=\"+bx+-+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "I believe that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+ ALIGN=MIDDLE  ALT=\"+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > serves as an amplitude while <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2pi%2Fb+ ALIGN=MIDDLE  ALT=\"+2pi%2Fb+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the period. (<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;\" >) is the horizontal shift and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the vertical shift. \r<BR>\n" );
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document.write( "What are the changes in the graph though? Thanks a lot.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677600 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > shifts the whole sine wave up or down<BR>\n" );
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;\" > enlarges or shrinks the sine wave<BR>\n" );
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;\" > shifts the sine wave to the right<BR>\n" );
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;\" > determines the period<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Here's 3 cases ( without the other variables )<BR>\n" );
document.write( "with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1%2F%282%2Api%29+ ALIGN=MIDDLE  ALT=\"+b+=+1%2F%282%2Api%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+2%2F%282%2Api%29+ ALIGN=MIDDLE  ALT=\"+b+=+2%2F%282%2Api%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+3%2F%282%2Api%29+ ALIGN=MIDDLE  ALT=\"+b+=+3%2F%282%2Api%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-8%2Api%2C+8%2Api%2C+-1.5%2C+1.5%2C+sin%281%2F%282%2Api%29%2Ax+%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-8%2Api%2C+8%2Api%2C+-1.5%2C+1.5%2C+sin%282%2F%282%2Api%29%2Ax+%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-8%2Api%2C+8%2Api%2C+-1.5%2C+1.5%2C+sin%283%2F%282%2Api%29%2Ax+%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "Here's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+pi%2F4+ ALIGN=MIDDLE  ALT=\"+c+=+pi%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+1%2F%282%2Api%29+ ALIGN=MIDDLE  ALT=\"+b+=+1%2F%282%2Api%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-6%2Api%2C+6%2Api%2C+-1.5%2C+1.5%2C+sin%281%2F%282%2Api%29%2Ax+-+pi%2F4+%29+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
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