document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084538>Question 1084538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sketch the graph of y=f(x)=|6-2x|+|x-1|-2x ,\r<BR>\n" );
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document.write( "what is the range of the function ? when is f(x)>0 ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698684 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=698684\">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=f%28x%29=abs%286-2x%29%2Babs%28x-1%29-2x ALIGN=MIDDLE  ALT=\"y=f%28x%29=abs%286-2x%29%2Babs%28x-1%29-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "graph: just do several points and draw a graph that looks like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2Cabs%286-2x%29%2Babs%28x-1%29-2x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2Cabs%286-2x%29%2Babs%28x-1%29-2x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the range of the function:\r<BR>\n" );
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document.write( "{ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=-4 ALIGN=MIDDLE  ALT=\"y%3E=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > }\r<BR>\n" );
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document.write( "when is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3E0+ ALIGN=MIDDLE  ALT=\"f%28x%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >? \r<BR>\n" );
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document.write( "first find zeros:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-2x+%2B+sqrt%28%28-2%28x-3%29%5E2%29%29+%2B+sqrt%28%28x+-1%29%5E2%29 ALIGN=MIDDLE  ALT=\"0+=+-2x+%2B+sqrt%28%28-2%28x-3%29%5E2%29%29+%2B+sqrt%28%28x+-1%29%5E2%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=0=-2x+%2B+-2%28x-+3%29+%2B+%28x+-+1%29 ALIGN=MIDDLE  ALT=\"0=-2x+%2B+-2%28x-+3%29+%2B+%28x+-+1%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=2x+=++-+2x%2B6%2B+x+-+1 ALIGN=MIDDLE  ALT=\"2x+=++-+2x%2B6%2B+x+-+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=2x+=+5+-+x ALIGN=MIDDLE  ALT=\"2x+=+5+-+x\"   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=2x%2Bx+=+5 ALIGN=MIDDLE  ALT=\"2x%2Bx+=+5\"   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=3x+=+5 ALIGN=MIDDLE  ALT=\"3x+=+5\"   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=x+=+5%2F3 ALIGN=MIDDLE  ALT=\"x+=+5%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=0=-2x+-%28-2%28x+-+3%29%29+%2B%28x+-+1%29 ALIGN=MIDDLE  ALT=\"0=-2x+-%28-2%28x+-+3%29%29+%2B%28x+-+1%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=0=-2x+%2B2%28x+-+3%29%29+%2Bx+-+1 ALIGN=MIDDLE  ALT=\"0=-2x+%2B2%28x+-+3%29%29+%2Bx+-+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=0=-2x+%2B2x+-+6+%2Bx+-1 ALIGN=MIDDLE  ALT=\"0=-2x+%2B2x+-+6+%2Bx+-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=0=+-+7+%2Bx+ ALIGN=MIDDLE  ALT=\"0=+-+7+%2Bx+\"   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=x+=+7 ALIGN=MIDDLE  ALT=\"x+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29%3E0+ ALIGN=MIDDLE  ALT=\"f%28x%29%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5%2F3 ALIGN=MIDDLE  ALT=\"+5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+infinity ALIGN=MIDDLE  ALT=\"+infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );