document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206973>Question 206973</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is horizontal asymptote and vertical asymptote of g(x)=5x/x^2-1? Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156488 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156488\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29+=+5x%2F%28x%5E2-1%29 ALIGN=MIDDLE  ALT=\"g%28x%29+=+5x%2F%28x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "if x = +/- 1 then x^2-1 = 0 so you will get a vertical asymptote at that point.<BR>\n" );
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document.write( "the vertical asymptote is when x approaches infinity but never quite reaches it ---<BR>\n" );
document.write( "the horizontal asymptote would be the value of y when x approaches infinity.<BR>\n" );
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document.write( "a good treatment of this subject can be found at:<BR>\n" );
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document.write( "http://www.purplemath.com/modules/asymptote.htm<BR>\n" );
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document.write( "a graph of your equation to show the vertical asymptotes is as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28400%2C400%2C-3%2C3%2C-10%2C10%2C5x%2F%28x%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"graph+%28400%2C400%2C-3%2C3%2C-10%2C10%2C5x%2F%28x%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "it appears that the horizontal asymptote is equal to 0 because as x approaches infinity, y approaches 0.<BR>\n" );
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document.write( "a graph of your equatrion to show the horizontal asymptotes is as follows:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28800%2C400%2C-40%2C40%2C-4%2C4%2C5x%2F%28x%5E2-1%29%29 ALIGN=MIDDLE  ALT=\"graph+%28800%2C400%2C-40%2C40%2C-4%2C4%2C5x%2F%28x%5E2-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "there is lots more information at the website i recommended so check it out if you need to know more.<BR>\n" );
document.write( "they also treat slanted asymptotes.<BR>\n" );
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document.write( "vertical asymptotes never cross the vertical line they approach.<BR>\n" );
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document.write( "horizontal asymptote can cross the horizontal line they approach.<BR>\n" );
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document.write( "enjoy<BR>\n" );
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