document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155779>Question 155779</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the follwing functions:<BR>\n" );
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document.write( "C) y= -|x-2|-10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114730 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=114730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%29=A ALIGN=MIDDLE  ALT=\"abs%28x%29=A\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=A ALIGN=MIDDLE  ALT=\"x=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-A ALIGN=MIDDLE  ALT=\"x=-A\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-2%29 ALIGN=MIDDLE  ALT=\"abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be broken up into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x-2%29=-x%2B2 ALIGN=MIDDLE  ALT=\"-%28x-2%29=-x%2B2\"   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=y=-abs%28x-2%29-10 ALIGN=MIDDLE  ALT=\"y=-abs%28x-2%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28x-2%29-10 ALIGN=MIDDLE  ALT=\"y=-%28x-2%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-2%29 ALIGN=MIDDLE  ALT=\"abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the first portion <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29 ALIGN=MIDDLE  ALT=\"%28x-2%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=y=-x%2B2-10 ALIGN=MIDDLE  ALT=\"y=-x%2B2-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-8 ALIGN=MIDDLE  ALT=\"y=-x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Now graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-8 ALIGN=MIDDLE  ALT=\"y=-x-8\"   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=graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-8 ALIGN=MIDDLE  ALT=\"y=-x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "---------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-abs%28x-2%29-10 ALIGN=MIDDLE  ALT=\"y=-abs%28x-2%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%28-x%2B2%29-10 ALIGN=MIDDLE  ALT=\"y=-%28-x%2B2%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x-2%29 ALIGN=MIDDLE  ALT=\"abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the second portion <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x%2B2%29 ALIGN=MIDDLE  ALT=\"%28-x%2B2%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=y=x-2-10 ALIGN=MIDDLE  ALT=\"y=x-2-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-12 ALIGN=MIDDLE  ALT=\"y=x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Now graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-12 ALIGN=MIDDLE  ALT=\"y=x-12\"   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=graph%28500%2C500%2C-10%2C10%2C-15%2C5%2Cx-12%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-15%2C5%2Cx-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-12 ALIGN=MIDDLE  ALT=\"y=x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now graph the two equations together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%2Cx-12%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%2Cx-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-x-8 ALIGN=MIDDLE  ALT=\"y=-x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (red). Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-12 ALIGN=MIDDLE  ALT=\"y=x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "Once again, since the sign out front the absolute value is negative, this means that the portion we keep is the negative portion that is below the point of intersection like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-abs%28x-2%29-10 ALIGN=MIDDLE  ALT=\"y=-abs%28x-2%29-10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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