document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=420081>Question 420081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with graphing rational funtions. <BR>\n" );
document.write( "The question is...Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes of each. Then sketch the graph. <BR>\n" );
document.write( "#1... F(X)= - 4/x^2-3x<BR>\n" );
document.write( "#2... f(x)= x-4/-4x-16<BR>\n" );
document.write( "#3... f(x)= x+4/-2x-6<BR>\n" );
document.write( "#4... f(x)= x^3-9x/3x^2-6x-9<BR>\n" );
document.write( "#5... f(x)= 3/x-2<BR>\n" );
document.write( "Please show me how to graph these equations. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293597 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=293597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Identify the points of discontinuity,holes,vertical asymptotes, and horizontal asmyptotes of each. Then sketch the graph. <BR>\n" );
document.write( "#1... F(X)= - 4/x^2-3x<BR>\n" );
document.write( "discont: x = 0 and x = 3<BR>\n" );
document.write( "holes: none<BR>\n" );
document.write( "vertical asympt : x = 0 and x = 3<BR>\n" );
document.write( "horizontal asympt: 0x^2/x^2 = 0/1 = 0 : Ans: y = 0<BR>\n" );
document.write( "------------------------------------------------------------<BR>\n" );
document.write( "#2... f(x)= x-4/-4x-16<BR>\n" );
document.write( "discont: x = -4<BR>\n" );
document.write( "holes: none<BR>\n" );
document.write( "v.a.:: x = -4<BR>\n" );
document.write( "h.a.:: x/(-4x) = 1/-4 : ans y = -1/4<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "#3... f(x)= x+4/-2x-6<BR>\n" );
document.write( "discont: x = -3<BR>\n" );
document.write( "holes: none<BR>\n" );
document.write( "va:: x = -3<BR>\n" );
document.write( "ha::x/-2x = -1/2: Ans: y = -1/2<BR>\n" );
document.write( "--------------------------------<BR>\n" );
document.write( "#4... f(x)= x^3-9x/3x^2-6x-9 = [x(x-3)(x+3)]/[3(x-3)(x+1)]<BR>\n" );
document.write( "disc: x = -1<BR>\n" );
document.write( "holes: x = 3<BR>\n" );
document.write( "va: x = -1<BR>\n" );
document.write( "ha: x^3/0x^3 = 1/0 = undefined : Ans: none<BR>\n" );
document.write( "--------------------------------------------<BR>\n" );
document.write( "#5... f(x)= 3/x-2<BR>\n" );
document.write( "disc: x = 2<BR>\n" );
document.write( "holes: none<BR>\n" );
document.write( "va: x = 2<BR>\n" );
document.write( "ha: 0x/x = 0/1 = 0 : Ans: y = 0<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );