document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136720>Question 1136720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the rational function f(x)= X^2+4X+3/2X+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #754526 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=754526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will assume you mean<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B3%29%2F%282x%2B4%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B4x%2B3%29%2F%282x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "and not<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B3%2F2x%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B3%2F2x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If you are working a problem like this, you should know that parentheses are required....<br><BR>\n" );
document.write( "(1) y-intercept: set x=0 --> 3/4<br><BR>\n" );
document.write( "(2) x-intercepts: where the function value is 0 -- i.e., where the numerator is 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x%2B3+=+%28x%2B1%29%28x%2B3%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x%2B3+=+%28x%2B1%29%28x%2B3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so x-intercepts at -3 and -1<br><BR>\n" );
document.write( "(3) horizontal asymptote: none (the degree of the numerator is 1 more than the degree of the denominator; the function has a (linear) oblique asymptote.<br><BR>\n" );
document.write( "(4) vertical asymptote: where the denominator is 0 -- at x=-2.<br><BR>\n" );
document.write( "Perform polynomial division to find the oblique asymptote:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2B4x%2B3%29%2F%282x%2B4%29+=+%28%28x%5E2%2B4x%2B4%29-1%29%2F%282x%2B4%29+=+%28%28x%2B2%29%5E2-1%29%2F%282%28x%2B2%29%29+=+%28x%2B2%29%2F2-1%2F%282%28x%2B2%29%29+=+%281%2F2%29x%2B1+-+1%2F%282x%2B4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The oblique asymptote is y = (1/2)x+1.<br><BR>\n" );
document.write( "A graph of the function and the oblique asymptote:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C3%2C-5%2C5%2C%28x%5E2%2B4x%2B3%29%2F%282x%2B4%29%2C%281%2F2%29x%2B1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );