document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583086>Question 583086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE help!  My teacher didn't explain.<BR>\n" );
document.write( "I have to write a rational function with the given asymptotes.\r<BR>\n" );
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document.write( "a. x=-2, y=0<BR>\n" );
document.write( "b. x=4,y=0<BR>\n" );
document.write( "c.x=2,x=1,y=1<BR>\n" );
document.write( "d.x=0,y= -1\r<BR>\n" );
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document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372344 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372344\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "A rational function has a vertical asymptote wherever the function is undefined, that is wherever the denominator is zero.  If the denominator is zero only when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -2\">, then a possible expression for your denominator is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\"> since <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ +\ 2\ =\ 0\"> iff <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ -2\">.  A more general expression that provides the same result is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x\ +\ 2)^n\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ \in\ \mathbb{N}\">.\r<BR>\n" );
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document.write( "A rational function has a horizontal asymptote of 0 only when the degree of the numerator is strictly less than the degree of the denominator.  For your specific case denominator above which has a degree of 1 you must have a numerator of degree zero, which is to say some constant. For the general case, your numerator must have a degree no greater than <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ -\ 1\">.\r<BR>\n" );
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document.write( "<i><b>Specific case:</i></b>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{C}{x\ +\ 2}\">\r<BR>\n" );
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document.write( "<i><b>General case:</i></b>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\sum_{i=0}^{n-1}\alpha_ix^{(n-1)-i}}{(x\ +\ 2)^n}\">\r<BR>\n" );
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document.write( "where at least one <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \alpha_k\ \neq\ 0\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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