document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=678483>Question 678483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find asymptotes? <BR>\n" );
document.write( "For example, y=1/x-2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #421447 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=421447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In general, the procedure for asymptotes is the following:\r<BR>\n" );
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document.write( "-set the denominator equal to zero and solve<BR>\n" );
document.write( "        the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zeroes ALIGN=MIDDLE  ALT=\"zeroes\"   DISABLED_style= \"max-width:90%; height:auto;\" > (if any) are the vertical asymptotes<BR>\n" );
document.write( "        everything else is the domain\r<BR>\n" );
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document.write( "-compare the degrees of the numerator and the denominator<BR>\n" );
document.write( "        if the degrees are the same, then you have a horizontal asymptote at \r<BR>\n" );
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document.write( "y = (numerator's leading coefficient) / (denominator's leading coefficient)<BR>\n" );
document.write( "        \r<BR>\n" );
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document.write( "if the denominator's degree is greater (by any margin), then you have a horizontal asymptote at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the x-axis)\r<BR>\n" );
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document.write( "        if the numerator's degree is greater (by a margin of 1), then you have a slant asymptote which you will find by doing long division\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=1%2F%28x-2%29 ALIGN=MIDDLE  ALT=\"y=1%2F%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The vertical asymptotes (and any restrictions on the domain) come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29=0\"   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;\" >.....so, domain is all <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;\" >\r<BR>\n" );
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document.write( "horizontal asymptote:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (the x-axis)\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+1%2F%28x-2%29%2C0%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+1%2F%28x-2%29%2C0%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and you can draw a line parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-axis ALIGN=MIDDLE  ALT=\"y-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the point <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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