document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084114>Question 1084114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Function: (x^2+x-12)/(x^2-4)<BR>\n" );
document.write( "Identify horizontal asymptote, vertical asymptote, x-intercepts, and holes. If possible, graph.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698171 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=698171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-12%29%2F%28x%5E2-4%29=%28%28x%2B4%29%28x-3%29%29%2F%28%28x%2B2%29%28x-2%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-12%29%2F%28x%5E2-4%29=%28%28x%2B4%29%28x-3%29%29%2F%28%28x%2B2%29%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It is clear that the function is not defined for x=2 and for x=-2.<BR>\n" );
document.write( "As x approaches those values the denominator approaches zero,<BR>\n" );
document.write( "while the numerator approaches some non-zero value.<BR>\n" );
document.write( "That means that as x approaches 2 or -2,<BR>\n" );
document.write( "the absolute value of the function increases without bounds.<BR>\n" );
document.write( "So, x=2, and x=z2 are vertical asymptotes.<BR>\n" );
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document.write( "Looking at the function a different way we see that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-12%29%2F%28x%5E2-4%29=%28%28x%5E2-4%29%2B%28x-8%29%29%2F%28x%5E2-4%29=%28x%5E2-4%29%2F%28x%5E2-4%29%2B%28x-8%29%2F%28x%5E2-4%29=1%2B%28x-8%29%2F%28x%5E2-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "we see that as the absolute value of x increases,<BR>\n" );
document.write( "the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-8%29%2F%28x%5E2-4%29 ALIGN=MIDDLE  ALT=\"%28x-8%29%2F%28x%5E2-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > approaches zero,<BR>\n" );
document.write( "meaning that the function's value approaches 1.<BR>\n" );
document.write( "So, y=1 is the horizontal asymptote. </SPAN>\n" );
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