document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061131>Question 1061131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> State the horizontal asymptote of the rational functions.<BR>\n" );
document.write( "(these were separate questions but I had to do the same thing on both.)<BR>\n" );
document.write( "f(x) = (7x^2 - 3x -9)/(2x^2 - 4x+5)\r<BR>\n" );
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document.write( "f(x) = (x+9)/(x^2+ 2x+5) \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675968 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39630)</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=675968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your second function and the question seem more interesting.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > has a sign change at x=-9.  Denominator is not factorable, and denominator is positive for all x values.\r<BR>\n" );
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document.write( "Think how the rational expression goes as x tends either toward negative infinity or toward positive infinity.  The denominator increases in size MORE THAN the numerator.  This function will become increasingly closer to 0 to the left, and become increasingly closer to zero to the right.  Horizontal asymptote is y=0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Same thing closer look:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-9%2C9%2C-3%2C3%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-9%2C9%2C-3%2C3%2C%28x%2B9%29%2F%28x%5E2%2B2x%2B5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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