document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818315>Question 818315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertical asymptotes, if any, of the graph of the rational function.\r<BR>\n" );
document.write( "\n" );
document.write( "f(x) = x/x^2+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492529 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=492529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the function is<BR>\n" );
document.write( "f(x) = x/x^2+4=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fx%5E2%2B4=1%2Fx%2B4 ALIGN=MIDDLE  ALT=\"x%2Fx%5E2%2B4=1%2Fx%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-5%2C5%2C-5%2C15%2Cx%2Fx%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-5%2C5%2C-5%2C15%2Cx%2Fx%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "there is a vertical asymptote, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the function is<BR>\n" );
document.write( "f(x) = x/(x^2+4)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-20%2C20%2C-0.5%2C0.5%2Cx%2F%28x%5E2%2B4%29%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-20%2C20%2C-0.5%2C0.5%2Cx%2F%28x%5E2%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "there is no vertical asymptote,<BR>\n" );
document.write( "because the denominator, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4 ALIGN=MIDDLE  ALT=\"x%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "is not zero for any real value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );