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 #372396 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=372396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How to find the end behavior of this function? <BR>\n" );
document.write( "x(2-x)(x+3)^2 <BR>\n" );
document.write( "**<BR>\n" );
document.write( "zeros are: 0, 2 and -3 (multi 2)<BR>\n" );
document.write( "Draw a number line with the zeros on it to show how the sign of f(x) changes as we go thru the zeros.\r<BR>\n" );
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document.write( "<..-...-3....-.....0.....+....2....-....>\r<BR>\n" );
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document.write( "When x is >2, f(x)<0<BR>\n" );
document.write( "Moving to the left, signs of the intervals switch as we go thru zeros of odd multiplicity like 1, 3, 5 etc. but do not switch when going thru zeros of even multiplicity like 2, 4, 6 etc. For this problem, 3 is of even multiplicity 2, while 0 and 2 are of odd multiplicity 1.<BR>\n" );
document.write( "You are right that as x approaches negative or positive infinity, f(x) approaches negative infinity. </SPAN>\n" );
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