document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5013>Question 5013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^3-x^2-6x divided by x^2-3x+2\r<BR>\n" );
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document.write( "I want to find:<BR>\n" );
document.write( "a)  Any zeros ____<BR>\n" );
document.write( "b)  vertical asymptotes ___<BR>\n" );
document.write( "c)  horizontal asymptotes___<BR>\n" );
document.write( "d) the domain of the function_______<BR>\n" );
document.write( "e) the range of the function____<BR>\n" );
document.write( "f) where f(x)is greater or = to 0: ________\r<BR>\n" );
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document.write( "this can be done by using a calculator but need steps to see how to do it.<BR>\n" );
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 #2499 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=2499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = (x^3-x^2-6x)<BR>\n" );
document.write( "       --------------<BR>\n" );
document.write( "       (x^2-3x+2)\r<BR>\n" );
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document.write( "I want to find:<BR>\n" );
document.write( "a)  Any zeros ____<BR>\n" );
document.write( "  The top: x^3-x^2-6x = x(x^2-x-6) = x(x-3)(x+2) = 0 --><BR>\n" );
document.write( "   x =0 or 3 or -2 (three zeros)<BR>\n" );
document.write( "b)  vertical asymptotes ___<BR>\n" );
document.write( "  Set the denominator x^2-3x+2 = 0 -->(x-2)(x-1) = 0 --><BR>\n" );
document.write( "  x -2 = 0 or x-1 = 0  (two vertical asymptotes)<BR>\n" );
document.write( "c)  horizontal asymptotes___<BR>\n" );
document.write( "  Set x-->+oo, f(x)--> x^3/x^2 -->+oo<BR>\n" );
document.write( "  So, no horizontal asymptotes<BR>\n" );
document.write( "d) the domain of the function_______<BR>\n" );
document.write( "  The denominator cannot be zero, so the domain<BR>\n" );
document.write( "  = R -{1,2} = (-oo,1)U(1,2)U(2,+OO)<BR>\n" );
document.write( "e) the range of the function____<BR>\n" );
document.write( "  f(x) = x(x-3)(x+2)<BR>\n" );
document.write( "       --------------<BR>\n" );
document.write( "       (x-2)(x-1)<BR>\n" );
document.write( "  f(x) can be any real numbers, so <BR>\n" );
document.write( "  the range of the function = R<BR>\n" );
document.write( "  <BR>\n" );
document.write( "f) where f(x)is >=: ________<BR>\n" );
document.write( " f(x) = x(x-3)(x+2)<BR>\n" );
document.write( "       --------------<BR>\n" );
document.write( "       (x-2)(x-1)<BR>\n" );
document.write( " f(x)>= 0 implies x(x-3)(x+2)(x-2)(x-1)>=0 rearrange to<BR>\n" );
document.write( " or (x-3)(x-2)(x-1)x(x+2)>=0 <BR>\n" );
document.write( " so, x>=3 or 1 < x < 2 or -2 <= x <= 0 {Note x cannot ben1 or 2)<BR>\n" );
document.write( " Expressed by intervals: [-2,0] U (1,2)U [3,+oo)\r<BR>\n" );
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document.write( " Important note: Forget to use any calculator to solve this<BR>\n" );
document.write( " kind of questions. <BR>\n" );
document.write( " Idea is crucial in math no calculations or the results.\r<BR>\n" );
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document.write( " Kenny </SPAN>\n" );
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