document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=768084>Question 768084</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)=3x/(x-4)(x+4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468053 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=468053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x%2F%28%28x-4%29%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"f%28x%29=3x%2F%28%28x-4%29%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Critical points at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-4 ALIGN=MIDDLE  ALT=\"x=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Also f crosses x axis at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The THREE critical points form four intervals of the horizontal x axis.  Vertical asymptotes at x=-4 and x=4.\r<BR>\n" );
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document.write( "INTERVALS_______________________SIGN<BR>\n" );
document.write( "(-infin, -4)________(-)/(- -)_________(-)<BR>\n" );
document.write( "(-4, 0)_____________(-)/(- +)_________(+)<BR>\n" );
document.write( "(0, +4)_____________(+)/(- +)_________(-)<BR>\n" );
document.write( "(+4, infin)_________(+)/(+ +)_________(+)\r<BR>\n" );
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