document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890057>Question 890057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How dou you find the domain and their vertical, horizontal or oblique asymptote?\r<BR>\n" );
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document.write( "r(x) = x^2+x-72/ x^2-x-56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538683 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</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=538683\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r(x) = x^2+x-72/ x^2-x-56\r<BR>\n" );
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document.write( "The correct text form you want is  r(x)=(x^2+x-72)/(x^2-x-56)\r<BR>\n" );
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document.write( "and as rendered looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=%28x%5E2%2Bx-72%29%2F%28x%5E2-x-56%29 ALIGN=MIDDLE  ALT=\"r%28x%29=%28x%5E2%2Bx-72%29%2F%28x%5E2-x-56%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor if you can.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=%28%28x-8%29%28x%2B9%29%29%2F%28%28x%2B7%29%28x-8%29%29 ALIGN=MIDDLE  ALT=\"r%28x%29=%28%28x-8%29%28x%2B9%29%29%2F%28%28x%2B7%29%28x-8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A discontinuity occurs at x=8.  This is because of the factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%2F%28x-8%29 ALIGN=MIDDLE  ALT=\"%28x-8%29%2F%28x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A vertical asymptote will occur at x=-7 because the function is undefined there.\r<BR>\n" );
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document.write( "Domain:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity%3Cx%3C-7 ALIGN=MIDDLE  ALT=\"-infinity%3Cx%3C-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > U  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7%3Cx%3C8 ALIGN=MIDDLE  ALT=\"-7%3Cx%3C8\"   DISABLED_style= \"max-width:90%; height:auto;\" > U  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%3Cx%3Cinfinity ALIGN=MIDDLE  ALT=\"8%3Cx%3Cinfinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\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-15%2C10%2C-15%2C10%2C%28x%5E2%2Bx-72%29%2F%28x%5E2-x-56%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C10%2C-15%2C10%2C%28x%5E2%2Bx-72%29%2F%28x%5E2-x-56%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph will not display properly the discontinuity at x=8 but it is there.  The HORIZONTAL asymptote is y=1.   This might be easier to understand if you take your original function before factoring and examine what happens for x extremely large or small without bound.  The x^2 terms in numerator and denominator become increasingly far more important, so each approaches the same square value, and you have the ratio of these. </SPAN>\n" );
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