document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152178>Question 152178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you identify the intercepts and asymptotes of this equation?\r<BR>\n" );
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document.write( "f(x) = (3x) / (x^2 + 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111964 by </B><A HREF=/tutors/aboutme.mpl?userid=mducky2><B>mducky2(62)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mducky2><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=111964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start with finding the y-intercept. When x is equal to 0, we know that the graph is crossing the y-axis. So, when we have x be 0 in the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%2F%28x%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"y+=+3x%2F%28x%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%280%29%2F%280%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"y+=+3%280%29%2F%280%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0%2F1 ALIGN=MIDDLE  ALT=\"y+=+0%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like the y-intercept is at y = 0.<BR>\n" );
document.write( "<br>Now let's find the x-intercept. When y is equal to 0, we know that the graph is crossing the x-axis. So, when we have y be 0 in the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%2F%28x%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"y+=+3x%2F%28x%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+3x%2F%28x%5E2+%2B+1%29 ALIGN=MIDDLE  ALT=\"0+=+3x%2F%28x%5E2+%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2A%28x%5E2+%2B+1%29+=+%28x%5E2+%2B+1%29%2A%283x%2F%28x%5E2+%2B+1%29%29+ ALIGN=MIDDLE  ALT=\"0%2A%28x%5E2+%2B+1%29+=+%28x%5E2+%2B+1%29%2A%283x%2F%28x%5E2+%2B+1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+3x ALIGN=MIDDLE  ALT=\"0+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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( "It looks like the x-intercept is at x = 0.<BR>\n" );
document.write( "<br>Now let's look for the asymptotes. An asymptote happens when the value of y is undefined. The easiest way to find an asymptote is for the bottom of the fraction to equal 0. In this case:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3x%2F%28x%5E2%2B1%29 ALIGN=MIDDLE  ALT=\"y+=+3x%2F%28x%5E2%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+1+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+-1 ALIGN=MIDDLE  ALT=\"x%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because the answer to this isn't a real number, there are no asymptotes. </SPAN>\n" );
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