document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027061>Question 1027061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the function: (x^3+2x^2-4x-8)/2x^2-8\r<BR>\n" );
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document.write( "a) Find the domain of the function, and discuss the behavior of f near any excluded x ­values.<BR>\n" );
document.write( "b) Identify all intercepts<BR>\n" );
document.write( "c) Find all vertical, horizontal, and slant asymptotes of the graph of the function. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642411 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=642411\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume you meant<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E3%2B2x%5E2-4x-8%29%2F%282x%5E2-8%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%5E3%2B2x%5E2-4x-8%29%2F%282x%5E2-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The numerator and denominator of that rational function can be factored.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%5E3%2B2x%5E2-4x-8%29%2F%282x%5E2-8%29=%28%28x%5E2-4%29%28x%2B2%29%29%2F2%28x%5E2-4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "When <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4=0 ALIGN=MIDDLE  ALT=\"x%5E2-4=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%7Bx=-2%2C%22or%22%2Cx=2%29 ALIGN=MIDDLE  ALT=\"system%7Bx=-2%2C%22or%22%2Cx=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the  denominator is zero,<BR>\n" );
document.write( "and the function has no defined value.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) So, the values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%7Bx=-2%2C%22and%22%2Cx=2%29 ALIGN=MIDDLE  ALT=\"system%7Bx=-2%2C%22and%22%2Cx=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are excluded from the domain of the function.<BR>\n" );
document.write( "The function can be simplified as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B2%29%2F2=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B2%29%2F2=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%7Bx%3C%3E-2%2C%22and%22%2Cx%3C%3E2%29 ALIGN=MIDDLE  ALT=\"system%7Bx%3C%3E-2%2C%22and%22%2Cx%3C%3E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .<BR>\n" );
document.write( "The graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a straight line with two holes,<BR>\n" );
document.write( "and the behavior of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > near the excluded values (and everywhere else in its domain)<BR>\n" );
document.write( "is just like the behavior of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%2B2%29%2F2=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%2B2%29%2F2=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E-2%2Cf%28x%29%29=%28-2%2B2%29%2F2=0 ALIGN=MIDDLE  ALT=\"lim%28x-%3E-2%2Cf%28x%29%29=%28-2%2B2%29%2F2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim%28x-%3E2%2Cf%28x%29%29=%282%2B2%29%2F2=2 ALIGN=MIDDLE  ALT=\"lim%28x-%3E2%2Cf%28x%29%29=%282%2B2%29%2F2=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "b) The y-intercept of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=%280%2B2%29%2F2=2%2F2=1 ALIGN=MIDDLE  ALT=\"f%280%29=%280%2B2%29%2F2=2%2F2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "or the point (0,1) .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is never zero, because where the function exists<BR>\n" );
document.write( "it is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=%28x%2B2%29%2F2 ALIGN=MIDDLE  ALT=\"g%28x%29=%28x%2B2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=0 ALIGN=MIDDLE  ALT=\"g%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > only for <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;\" > which is not part of the domain of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, there is no x-intercept. The graph of function does not intersect the x-axis; it jumps over it.<BR>\n" );
document.write( " <BR>\n" );
document.write( "c) Since everywhere in its domain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"f%28x%29=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F2%29x%2B1 ALIGN=MIDDLE  ALT=\"y=%281%2F2%29x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > could be considered the slant asymptote. There is no other asymptote. </SPAN>\n" );
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