document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=583247>Question 583247</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How to find the end behavior of this function?\r<BR>\n" );
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document.write( "x(2-x)(x+3)^2\r<BR>\n" );
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document.write( "would it be: as x approaches positive or negative infinity, y approaches negative infinity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #372390 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=372390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "First of all, if you are going to say that it is a function, write it like a function, namely:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x(2\ -\ x)(x\ +\ 3)^2\">\r<BR>\n" );
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document.write( "Then re-write to expand the squared binomial:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ x(2\ -\ x)(x\ +\ 3)(x\ +\ 3)\">\r<BR>\n" );
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document.write( "Now, evaluate each of the factors for its sign if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> is a relatively large positive number, say 100.\r<BR>\n" );
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document.write( "First factor is +<BR>\n" );
document.write( "Second factor is -<BR>\n" );
document.write( "Third factor is +<BR>\n" );
document.write( "Fourth factor is +\r<BR>\n" );
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document.write( "Plus times Minus times Plus times Plus is Minus.  As <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> increases without bound, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ \right\ \infty\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> decreases without bound, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ \right\ -\infty\">.\r<BR>\n" );
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document.write( "Repeat the process with a relatively large negative number, -100 should do nicely:\r<BR>\n" );
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document.write( "First factor is -<BR>\n" );
document.write( "Second factor is +<BR>\n" );
document.write( "Third factor is -<BR>\n" );
document.write( "Fourth factor is -\r<BR>\n" );
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document.write( "Minus times Plus times Minus times Minus is Minus.  As <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\"> decreases without bound, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x\ \right\ -\infty\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\"> decreases without bound, i.e. <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE y\ \right\ -\infty\">.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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