document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=498503>Question 498503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph this rational function. Start by combining all terms over a common denominator.<BR>\n" );
document.write( "            \r<BR>\n" );
document.write( "\n" );
document.write( "R(x)=2/3+28/3x+16/x^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #337271 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=337271\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph this rational function. Start by combining all terms over a common denominator.<BR>\n" );
document.write( "R(x)=2/3+28/3x+16/x^2<BR>\n" );
document.write( "**<BR>\n" );
document.write( "R(x)=2/3+28/3x+16/x^2<BR>\n" );
document.write( "LCD: 3x^2<BR>\n" );
document.write( "R(x)=(2x^2+28x+48)/3x^2<BR>\n" );
document.write( "R(x)=2(x^2+14x+24)/3x^2<BR>\n" );
document.write( "2(x+12)(x+2)/3x^2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "y-intercept<BR>\n" );
document.write( "Set x=0, then solve for y<BR>\n" );
document.write( "When x=0, function becomes undefined<BR>\n" );
document.write( "y-intercept: none<BR>\n" );
document.write( "..<BR>\n" );
document.write( "x-intercept<BR>\n" );
document.write( "set y=0, then solve for x<BR>\n" );
document.write( "2(x^2+14x+24)=0<BR>\n" );
document.write( "2(x+12)(x+2)=0<BR>\n" );
document.write( "x-intercepts: -12 and -2<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Horizontal Asymptote:<BR>\n" );
document.write( "Since degree of numerator=degree of denominator, divide lead coefficient of numerator(2) by lead coefficient of denominator(3)=2/3<BR>\n" );
document.write( "Horizontal Asymptote: 2/3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Vertical Asymptote:<BR>\n" );
document.write( "Set denominator=0, then solve for x<BR>\n" );
document.write( "3x^2=0<BR>\n" );
document.write( "x=0<BR>\n" );
document.write( "Vertical Asymptote: x=0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "number line of function:<BR>\n" );
document.write( "<...+...-12...-...-2.....+....0......+......><BR>\n" );
document.write( "I don't have the means to draw a detailed graph of the given function, but I have provided all the information you need to draw one.  See the graph below as a visual check on the answers.\r<BR>\n" );
document.write( "\n" );
document.write( "..<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C10%2C+-10%2C+10%2C2%2F3%2B28%2F3x%2B16%2Fx%5E2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C10%2C+-10%2C+10%2C2%2F3%2B28%2F3x%2B16%2Fx%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );