document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44651>Question 44651</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Find the vertical asymptote of the rational function f(x)=3x-12/4x-2.\r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29542 by </B><A HREF=/tutors/aboutme.mpl?userid=adamchapman><B>adamchapman(301)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=adamchapman><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=29542\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An asymptote is an imaginargy line on a graoh that plots points where the value of the function is impossible to determine. A verticle asymptote on an x-y graph would have a line equation of the form x=_.<BR>\n" );
document.write( "Let's look at your function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%283x-12%29%2F%284x-2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%283x-12%29%2F%284x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We know that it is impossible to divide something by zero. Try it on your calculator. You will get some kind of error message.<BR>\n" );
document.write( "So the asymptote of the function f(x) must occur when the denominator is equal to zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x-2=0 ALIGN=MIDDLE  ALT=\"4x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=2 ALIGN=MIDDLE  ALT=\"4x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2F4 ALIGN=MIDDLE  ALT=\"x=2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F2 ALIGN=MIDDLE  ALT=\"x=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the verticle asymptote of f(x) is x=1/2.<BR>\n" );
document.write( "Note on the graph below that it is impossible to determine the value of y when x=1/2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+300%2C+200%2C+-6%2C+5%2C+-15%2C+15%2C+%283x-12%29%2F%284x-2%29%29+ ALIGN=MIDDLE  ALT=\"graph%28+300%2C+200%2C+-6%2C+5%2C+-15%2C+15%2C+%283x-12%29%2F%284x-2%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I hope this helps.<BR>\n" );
document.write( "P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk<BR>\n" );
document.write( "Adam\r<BR>\n" );
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