document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128268>Question 128268</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618250204/algebrahomeworkh>Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do i identify horizontal and vertical asymptotes of functions<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 #93912 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=93912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Vertical asymptotes occur where the denominator of a rational function are zero.<BR>\n" );
document.write( "There is an exception to this, however.  If a rational function has the same<BR>\n" );
document.write( "factor in numberator and denominator there is a hole in the finction, not <BR>\n" );
document.write( "a vertical asymptote.<BR>\n" );
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document.write( "Horizontal asymptote occurs in a rational function where y = p/q,<BR>\n" );
document.write( "where p and q are the coefficient of the highest power term that<BR>\n" );
document.write( "occurs in the numerator OR the denominator.<BR>\n" );
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document.write( "Example:<BR>\n" );
document.write( "f(x) = [(x-3)(x+2)]/[(x+2)(2x+5)]<BR>\n" );
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document.write( "Hole: at x=-2 because there is a factor of (x+2) in numerator and denominator.<BR>\n" );
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document.write( "Vertical Asymptote: at x = -5/2 because (2x+5) is in the denominator.<BR>\n" );
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document.write( "Horizontal Asymptote: at y = 1/2 because the highest power term in numerator<BR>\n" );
document.write( "and denominator is x^2; you have 1x^2/2x^2 = 1/2<BR>\n" );
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document.write( "Hope this helps.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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