document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=948369>Question 948369</A>: <I><SPAN STYLE=\"word-break: break-all;\"> state the intervals where the function is increasing, decreasing, or constant.\r<BR>\n" );
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document.write( "The function is: f(x)=-1|x-2|+2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #578880 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=578880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The critical value is at x=2.  The function is split to two branches around x=2.\r<BR>\n" );
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document.write( "CASE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C2 ALIGN=MIDDLE  ALT=\"x%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%28abs%28x-2%29%29%2B2 ALIGN=MIDDLE  ALT=\"-1%28abs%28x-2%29%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2A%28-1%29%28x-2%29%2B2 ALIGN=MIDDLE  ALT=\"-1%2A%28-1%29%28x-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2%3C0 ALIGN=MIDDLE  ALT=\"x-2%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%2B2 ALIGN=MIDDLE  ALT=\"%28x-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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" );
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document.write( "CASE  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-1%28x-2%29%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29=-1%28x-2%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B2%2B2 ALIGN=MIDDLE  ALT=\"-x%2B2%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%2B4 ALIGN=MIDDLE  ALT=\"-x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Definition for f:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x ALIGN=MIDDLE  ALT=\"f%28x%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C2 ALIGN=MIDDLE  ALT=\"x%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and f is increasing.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-x%2B4 ALIGN=MIDDLE  ALT=\"f%28x%29=-x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=2 ALIGN=MIDDLE  ALT=\"x%3E=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and f is decreasing  (see the negative slope).<BR>\n" );
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document.write( "Sometimes my work appears to skip a step.<BR>\n" );
document.write( "Be aware of this idea:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a-b ALIGN=MIDDLE  ALT=\"a-b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an expression;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a-b%29=-1%2A%28a-b%29 ALIGN=MIDDLE  ALT=\"-%28a-b%29=-1%2A%28a-b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2Aa-%28-1%29b ALIGN=MIDDLE  ALT=\"-1%2Aa-%28-1%29b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2Bb ALIGN=MIDDLE  ALT=\"-a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-a ALIGN=MIDDLE  ALT=\"b-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Shorter,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28a-b%29=b-a ALIGN=MIDDLE  ALT=\"-%28a-b%29=b-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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