document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=659376>Question 659376</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=x-3  <BR>\n" );
document.write( "Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410776 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=410776\">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=y=x-3 ALIGN=MIDDLE  ALT=\"y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >, check to see if it is the same when you replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-3+=+x-3 ALIGN=MIDDLE  ALT=\"-x-3+=+x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1-3+=+1-3 ALIGN=MIDDLE  ALT=\"-1-3+=+1-3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C%3E+-2 ALIGN=MIDDLE  ALT=\"-4+%3C%3E+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x-3 ALIGN=MIDDLE  ALT=\"y+=+x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > have symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "2. symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "For symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >, check to see if it is the same when you replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y ALIGN=MIDDLE  ALT=\"-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y+=+-x%2B3 ALIGN=MIDDLE  ALT=\"-y+=+-x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8800; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x-3 ALIGN=MIDDLE  ALT=\"y+=+x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > have symmetry about the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "3. diagonal symmetry\r<BR>\n" );
document.write( "\n" );
document.write( "For diagonal symmetry, check to see if it is the same when you swap <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y-3 ALIGN=MIDDLE  ALT=\"x=y-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...=>.. is not the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-3 ALIGN=MIDDLE  ALT=\"y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-3 ALIGN=MIDDLE  ALT=\"y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > have diagonal symmetry\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4. origin symmetry\r<BR>\n" );
document.write( "\n" );
document.write( "Start with:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-3 ALIGN=MIDDLE  ALT=\"y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x ALIGN=MIDDLE  ALT=\"-x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y ALIGN=MIDDLE  ALT=\"-y\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y=-x-3 ALIGN=MIDDLE  ALT=\"-y=-x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1 ALIGN=MIDDLE  ALT=\"-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-y%2A-1=-x%2A%28-1%29-3+%28-1%29 ALIGN=MIDDLE  ALT=\"-y%2A-1=-x%2A%28-1%29-3+%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3+ ALIGN=MIDDLE  ALT=\"y=x%2B3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "we have the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3 ALIGN=MIDDLE  ALT=\"y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-3 ALIGN=MIDDLE  ALT=\"y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , hence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=x-3 ALIGN=MIDDLE  ALT=\"+y=x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NOT ALIGN=MIDDLE  ALT=\"NOT\"   DISABLED_style= \"max-width:90%; height:auto;\" > have origin symmetry\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+x-3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+x-3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );