document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155778>Question 155778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the follwing functions:<BR>\n" );
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document.write( "B) y= -|x+10|-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #114729 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=114729\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Remember, 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 means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B10%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B10%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%2B10%29 ALIGN=MIDDLE  ALT=\"%28x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%2B10%29=-x-10 ALIGN=MIDDLE  ALT=\"-%28x%2B10%29=-x-10\"   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%2B10%29-2 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B10%29-2\"   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%2B10%29-2 ALIGN=MIDDLE  ALT=\"y=-%28x%2B10%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B10%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B10%29 ALIGN=MIDDLE  ALT=\"%28x%2B10%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-10-2 ALIGN=MIDDLE  ALT=\"y=-x-10-2\"   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 let's 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-15%2C5%2C-12%2C8%2C-x-12%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-x-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( "--------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-abs%28x%2B10%29-2 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B10%29-2\"   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-10%29-2 ALIGN=MIDDLE  ALT=\"y=-%28-x-10%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B10%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x-10%29 ALIGN=MIDDLE  ALT=\"%28-x-10%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%2B10-2 ALIGN=MIDDLE  ALT=\"y=x%2B10-2\"   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%2B8 ALIGN=MIDDLE  ALT=\"y=x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Now let's graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B8 ALIGN=MIDDLE  ALT=\"y=x%2B8\"   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-15%2C5%2C-12%2C8%2Cx%2B8%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-15%2C5%2C-12%2C8%2Cx%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B8 ALIGN=MIDDLE  ALT=\"y=x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's graph the two equations on the same coordinate system:\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-15%2C5%2C-12%2C8%2C-x-12%2Cx%2B8%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-x-12%2Cx%2B8%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;\" > (red). Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B8 ALIGN=MIDDLE  ALT=\"y=x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "Now since the sign in front of the absolute value is negative, this means that we only need to worry about the negative portion. So this means that we have to erase the portions of the graph that are above the 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-15%2C5%2C-12%2C8%2C-abs%28x%2B10%29-2%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-abs%28x%2B10%29-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-abs%28x%2B10%29-2 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B10%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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%2B10%29-2 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B10%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is \r<BR>\n" );
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