document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=911752>Question 911752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help with the x-intercept and vertical asymptote of rational functions\r<BR>\n" );
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document.write( "VA = I have no idea <BR>\n" );
document.write( "HA = 4? <BR>\n" );
document.write( "x-int = no idea <BR>\n" );
document.write( "y-int = 0,-32 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820x%5E2%2B20x-40%29%2F%28x%5E2%2Bx%29 ALIGN=MIDDLE  ALT=\"%2820x%5E2%2B20x-40%29%2F%28x%5E2%2Bx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "VA = no idea <BR>\n" );
document.write( "HA = 20? <BR>\n" );
document.write( "x-int = no idea <BR>\n" );
document.write( "y-int = 0,-40 \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%5E2%29%2F%28x%5E2-2x-63%29 ALIGN=MIDDLE  ALT=\"%286x%5E2%29%2F%28x%5E2-2x-63%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "VA = -7,9 <BR>\n" );
document.write( "HA = 6 <BR>\n" );
document.write( "x-int = no idea <BR>\n" );
document.write( "y-int = 0,-63 \r<BR>\n" );
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document.write( "Please make any corrections and help with the missing ones. <BR>\n" );
document.write( "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 #553326 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</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=553326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Notice that each example uses numerators and denominators of degree 2.  This is an indication, the degree of numerator and denominator equal, of the rational expression having a horizontal asymptote.\r<BR>\n" );
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document.write( "Doing ONLY your first example:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%28x%5E2%2B18x%2B80%29%29%2F%28%28x%2B10%29%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%284%28x%5E2%2B18x%2B80%29%29%2F%28%28x%2B10%29%28x-1%29%29\"   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=%284%28x%2B8%29%28x%2B10%29%29%2F%28%28x-1%29%28x%2B10%29%29 ALIGN=MIDDLE  ALT=\"%284%28x%2B8%29%28x%2B10%29%29%2F%28%28x-1%29%28x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Vertical Asymptote at x=1, because function will there be undefined.\r<BR>\n" );
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document.write( "Removed Point at x=-10, a hole in the graph, because you have a factor of 1=(x+10)/(x+10) which is undefined for x=-10.\r<BR>\n" );
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document.write( "x-intercept is VERY OBVIOUSLY at x=-8.  The function will be equal to 0 for x=-8.\r<BR>\n" );
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document.write( "You were unsure about horizontal asymptote, but what value you reported makes sense.  You could try multiplying numerator AND denominator by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx%5E2 ALIGN=MIDDLE  ALT=\"1%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and ponder how each term behaves as x tends to the right or to the left without bound.  The leading terms will make the rational expression approach 4, as you reported; since the nonleading terms approach zero, and you have something resembling <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F1 ALIGN=MIDDLE  ALT=\"4%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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