document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=725321>Question 725321</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given the rational function<BR>\n" );
document.write( "r(x)=(x^3-x^2)/x^3-3x-2)<BR>\n" );
document.write( "find the x and y intercepts<BR>\n" );
document.write( "find the vertical and horizontal asymptotes<BR>\n" );
document.write( "sketch the graph of r(x)<BR>\n" );
document.write( "state the domain and range of r(x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #444141 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=444141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given the rational function<BR>\n" );
document.write( "r(x)=(x^3-x^2)/(x^3-3x-2)<BR>\n" );
document.write( "find the x and y intercepts<BR>\n" );
document.write( "find the vertical and horizontal asymptotes<BR>\n" );
document.write( "sketch the graph of r(x)<BR>\n" );
document.write( "state the domain and range of r(x)<BR>\n" );
document.write( "***<BR>\n" );
document.write( "y-intercept:<BR>\n" );
document.write( "set x=0<BR>\n" );
document.write( "y=0<BR>\n" );
document.write( ".. <BR>\n" );
document.write( "x-intercept<BR>\n" );
document.write( "set x=0<BR>\n" );
document.write( "x^3-x^2=0<BR>\n" );
document.write( "x^2(x-1)=0<BR>\n" );
document.write( "x=0 (multiplicity 2)<BR>\n" );
document.write( "or<BR>\n" );
document.write( "x=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Horizontal asymptotes:<BR>\n" );
document.write( "When degree of numerator and denominator the same, divide lead coefficient of numerator by lead coefficient of denominator to determine horizontal asymptote.<BR>\n" );
document.write( "Horizontal asymptote: y=1/1=1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Vertical asymptotes:<BR>\n" );
document.write( "set denominator=0, then solve for x-values which make the function undefined.<BR>\n" );
document.write( "x^3-3x-2=0<BR>\n" );
document.write( "use rational roots theorem or graphing calculator to find x-values:<BR>\n" );
document.write( "x&#8800;-1 (multiplicity 2)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x&#8800;2<BR>\n" );
document.write( "Vertical asymptotes: x=-1 ,2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Domain: (-&#8734;,&#8734;)<BR>\n" );
document.write( "Range: (-&#8734;,&#8734;)\r<BR>\n" );
document.write( "\n" );
document.write( "Number Line:<BR>\n" );
document.write( "<...+..-1...+....0...-....1..-....2...+....><BR>\n" );
document.write( "see graph below\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%28x%5E3-x%5E2%29%2F%28x%5E3-3x-2%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%28x%5E3-x%5E2%29%2F%28x%5E3-3x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );