document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=771271>Question 771271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Analyze and graph the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2Bx-12%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-12%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Please provide the steps I must take in order to solve this.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470190 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=470190\">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%2B2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2Bx-12%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > fully factorable to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B4%29%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B4%29%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Performing polynomial division of the expression in the originally given form, the quotient will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1-10%2F%28x%2B2%29 ALIGN=MIDDLE  ALT=\"x-1-10%2F%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, giving a slant asymptote of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x-1 ALIGN=MIDDLE  ALT=\"y=x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   Vertical asymtpote is at <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;\" > becasue the denominator must not be zero  (the denominator of the given expression).\r<BR>\n" );
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document.write( "Two zeros occur:  x=-4, and x=3 are the zeros of the function.  \r<BR>\n" );
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document.write( "Critical points are x at -4, -2, and 3.  These are the intervals along the horizontal axis.  ...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3C-4 ALIGN=MIDDLE  ALT=\"x%3C-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%3Cx-2 ALIGN=MIDDLE  ALT=\"-4%3Cx-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3Cx%3C3 ALIGN=MIDDLE  ALT=\"-2%3Cx%3C3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%3Cx ALIGN=MIDDLE  ALT=\"3%3Cx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What you want to do is test any x value in each interval and find if the function is positive or negative.  I omit that part of the analysis, but this is the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-8%2C8%2C-8%2C8%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-8%2C8%2C-8%2C8%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "OR THIS\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28500%2C500%2C-15%2C15%2C-15%2C15%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29 ALIGN=MIDDLE  ALT=\"graph%28500%2C500%2C-15%2C15%2C-15%2C15%2C%28x%5E2%2Bx-12%29%2F%28x%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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