document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=155782>Question 155782</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the follwing functions:<BR>\n" );
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document.write( "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 #114732 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=114732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Note: the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B2%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be broken into the expressions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28x%2B2%29=-x-2 ALIGN=MIDDLE  ALT=\"-%28x%2B2%29=-x-2\"   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%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B2%29%2B10\"   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%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-%28x%2B2%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B2%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%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%2B10 ALIGN=MIDDLE  ALT=\"y=-x-2%2B10\"   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 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-10%2C10%2C-8%2C12%2C-x%2B8%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-x%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( "------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-abs%28x%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B2%29%2B10\"   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-2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-%28-x-2%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > Replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28x%2B2%29 ALIGN=MIDDLE  ALT=\"abs%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x-2%29 ALIGN=MIDDLE  ALT=\"%28-x-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%2B10 ALIGN=MIDDLE  ALT=\"y=x%2B2%2B10\"   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%2B12 ALIGN=MIDDLE  ALT=\"y=x%2B12\"   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%2B12 ALIGN=MIDDLE  ALT=\"y=x%2B12\"   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-8%2C12%2Cx%2B12%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-8%2C12%2Cx%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B12 ALIGN=MIDDLE  ALT=\"y=x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So together the graphs are \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-8%2C12%2C-x%2B8%2Cx%2B12%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-x%2B8%2Cx%2B12%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;\" > (red) and graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B12 ALIGN=MIDDLE  ALT=\"y=x%2B12\"   DISABLED_style= \"max-width:90%; height:auto;\" > (green)\r<BR>\n" );
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document.write( "Since the leading sign on the absolute value is negative, this means that we'll erase the upper portion of the graph and keep the bottom portion 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-8%2C12%2C-abs%28x%2B2%29%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-abs%28x%2B2%29%2B10%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%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B2%29%2B10\"   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%2B2%29%2B10 ALIGN=MIDDLE  ALT=\"y=-abs%28x%2B2%29%2B10\"   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-8%2C12%2C-abs%28x%2B2%29%2B10%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-abs%28x%2B2%29%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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