document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177854>Question 1177854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x)= x-5 (divied by) 4-x^2\r<BR>\n" );
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document.write( "x - intercept(s): <BR>\n" );
document.write( "y - intercept: <BR>\n" );
document.write( "Vertical Asymptote(s): \r<BR>\n" );
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document.write( "Horizontal Asymptote(s):<BR>\n" );
document.write( "Domain: \r<BR>\n" );
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document.write( "End-Behavior: \r<BR>\n" );
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document.write( "Intervals of Increasing/Decreasing:<BR>\n" );
document.write( " <BR>\n" );
document.write( "Intervals of Positive/Negative: <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806988 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=806988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x - intercept(s):\r<BR>\n" );
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document.write( "set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0+ ALIGN=MIDDLE  ALT=\"f%28x%29=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2F%284-x%5E2%29=0 ALIGN=MIDDLE  ALT=\"%28x-5%29%2F%284-x%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........since denominator cannot be zero, use numerator only\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x - intercept is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "y - intercept:<BR>\n" );
document.write( "set <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%280-5%29%2F%284-0%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%280-5%29%2F%284-0%5E2%29\"   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=+-5%2F4 ALIGN=MIDDLE  ALT=\"f%28x%29=+-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y - intercept is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F4 ALIGN=MIDDLE  ALT=\"-5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Vertical Asymptote(s):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......set denominator equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-x%5E2%29=0 ALIGN=MIDDLE  ALT=\"%284-x%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4=x%5E2 ALIGN=MIDDLE  ALT=\"4=x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=2 ALIGN=MIDDLE  ALT=\"+x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Horizontal Asymptote(s):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=+%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=+%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Degree of numerator is less than degree of denominator: horizontal asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+0 ALIGN=MIDDLE  ALT=\"f%28x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Domain:<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;\" > element <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E-2+ ALIGN=MIDDLE  ALT=\"x%3C%3E-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C%3E2 ALIGN=MIDDLE  ALT=\"x%3C%3E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > }<BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3Cx%3C2 ALIGN=MIDDLE  ALT=\"-2%3Cx%3C2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "range:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=y ALIGN=MIDDLE  ALT=\"f%28x%29=y\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=+%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"y=+%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rewrite the above equation for x in standard form and solve using quadratic formulae<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%284-x%5E2%29=+%28x-5%29 ALIGN=MIDDLE  ALT=\"y%284-x%5E2%29=+%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y-yx%5E2=+x-5 ALIGN=MIDDLE  ALT=\"4y-yx%5E2=+x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+yx%5E2%2Bx-4y-5 ALIGN=MIDDLE  ALT=\"0=+yx%5E2%2Bx-4y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+yx%5E2%2Bx-%284y%2B5%29 ALIGN=MIDDLE  ALT=\"0=+yx%5E2%2Bx-%284y%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> a=y, b=1, c=-(4y+5)<BR>\n" );
document.write( "Find the discriminant to the above equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=1-4%2Ay%28-%284y%2B5%29%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=1-4%2Ay%28-%284y%2B5%29%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%2B16%2Ay%5E2%2B20y ALIGN=MIDDLE  ALT=\"1%2B16%2Ay%5E2%2B20y\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ".............=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Ay%5E2%2B20y+%2B1 ALIGN=MIDDLE  ALT=\"16%2Ay%5E2%2B20y+%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using the quadratic formulas, the above equation gives the solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D=%281%2B-sqrt%2816%2Ay%5E2%2B20y+%2B1%29%29%2F2y ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D=%281%2B-sqrt%2816%2Ay%5E2%2B20y+%2B1%29%29%2F2y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solutions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%2C2%5D ALIGN=MIDDLE  ALT=\"x%5B1%2C2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are real if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Ay%5E2%2B20y+%2B1++%3E=++0 ALIGN=MIDDLE  ALT=\"16%2Ay%5E2%2B20y+%2B1++%3E=++0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" >≠<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Hence we need to solve the inequality<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Ay%5E2%2B20y+%2B1+%3E=+0 ALIGN=MIDDLE  ALT=\"16%2Ay%5E2%2B20y+%2B1+%3E=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solution will be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=+%28sqrt%2821%29+-+5%29%2F8 ALIGN=MIDDLE  ALT=\"y%3E=+%28sqrt%2821%29+-+5%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3C=+%28-5+-+sqrt%2821%29%29%2F8 ALIGN=MIDDLE  ALT=\"y%3C=+%28-5+-+sqrt%2821%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "End-Behavior:\r<BR>\n" );
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document.write( "function end-behavior of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%3Einfinity ALIGN=MIDDLE  ALT=\"x-%3Einfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+-%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29+-%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and<BR>\n" );
document.write( "as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-%3E-infinity ALIGN=MIDDLE  ALT=\"x-%3E-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29-%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29-%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intervals of Increasing/Decreasing:<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%29%3E0 ALIGN=MIDDLE  ALT=\"%28x+%29%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28x+%29 ALIGN=MIDDLE  ALT=\"f+%28x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is increasing <BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%29%3C0 ALIGN=MIDDLE  ALT=\"%28x+%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+%28x+%29+ ALIGN=MIDDLE  ALT=\"f+%28x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is decreasing \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-5%29%2F%284-x%5E2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-5%29%2F%284-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...derivate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29+=+%28x%5E2+-+10+x+%2B+4%29%2F%28x%5E2+-+4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%29+=+%28x%5E2+-+10+x+%2B+4%29%2F%28x%5E2+-+4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Increasing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity+%3C+x+%3C-2 ALIGN=MIDDLE  ALT=\"-infinity+%3C+x+%3C-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C+x+%3C-sqrt%2821%29%2B5 ALIGN=MIDDLE  ALT=\"-2%3C+x+%3C-sqrt%2821%29%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "Decreasing:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-sqrt%2821%29%2B5+%3C+x+%3C+2 ALIGN=MIDDLE  ALT=\"-sqrt%2821%29%2B5+%3C+x+%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intervals of Positive/Negative:\r<BR>\n" );
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document.write( "positive when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-infinity+%3C+x%3C+-2+ ALIGN=MIDDLE  ALT=\"+-infinity+%3C+x%3C+-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > U  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%3C+x+%3C+infinity+ ALIGN=MIDDLE  ALT=\"2%3C+x+%3C+infinity+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "negative when  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C+x%3C+2 ALIGN=MIDDLE  ALT=\"-2%3C+x%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/qD3JJt0\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/qD3JJt0/download.png\" alt=\"download\" border=\"0\"></a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );