document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40809>Question 40809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the interval over which f(x)= the absolute value x-4 - the absolute value x+5 is a constant function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26675 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26675\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = |x-4| - |x+5|\r<BR>\n" );
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document.write( "When x<-5, |x-4| = -(x-4) = 4-x and |x+5| = -(x+5) = -x-5<BR>\n" );
document.write( "So f(x) = |x-4| - |x+5| = 4-x+x+5 = 9 \r<BR>\n" );
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document.write( "When -5<x<4, |x-4| = -(x-4) = 4-x and |x+5| = x+5<BR>\n" );
document.write( "So f(x) = |x-4| - |x+5| = 4-x-x-5 = -2x-1\r<BR>\n" );
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document.write( "When 4<x, |x-4| = x-4 and |x+5| = x+5<BR>\n" );
document.write( "So f(x) = |x-4| - |x+5| = x-4-x-5 = -9\r<BR>\n" );
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document.write( "When x = -5, f(x) = |-5-4| = 9<BR>\n" );
document.write( "When x = 4, f(x) = - |4+5| = -9\r<BR>\n" );
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document.write( "So f(x) = 9 when x <= -5<BR>\n" );
document.write( "and f(x) = -9 when x >= 4\r<BR>\n" );
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document.write( "Thus the interval in which f(x) is constant is x <= -5 and x >= 4. </SPAN>\n" );
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