document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=693925>Question 693925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I do not understand why does the graph of a rational have only one horizontal asymptote? Im familair kind of with something called an arbitrary function but that means some sort of way it can have two functions. Im extremely confused please help me. Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427642 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=427642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I do not understand why does the graph of a rational have only one horizontal asymptote? Im familair kind of with something called an arbitrary function but that means some sort of way it can have two functions. Im extremely confused please help me. Thank you in advance.<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "The numerator can only have one highest power term and that term can<BR>\n" );
document.write( "only have one coefficient.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "The same is true for the denominator.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "If the ratio of those coefficients is p/q, the horizontal asymptote<BR>\n" );
document.write( "is y = p/q so long as the degree of the numerator is not greater<BR>\n" );
document.write( "than the degree of the denominator.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Example:<BR>\n" );
document.write( "y = 3x^2/x <BR>\n" );
document.write( "p/q = 3/0<BR>\n" );
document.write( "No horizontal asymptote<BR>\n" );
document.write( "Will have slant asymptote<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = x/(3x^2)<BR>\n" );
document.write( "p/q = 1/3<BR>\n" );
document.write( "HA: y = 1/3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y = 3x^2/x^2 <BR>\n" );
document.write( "p/q = 3/1<BR>\n" );
document.write( "HA: y = 3<BR>\n" );
document.write( "==================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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