document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92223>Question 92223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.<BR>\n" );
document.write( "a. <BR>\n" );
document.write( "f(x) = 2x + 3/x + 3\r<BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "g(x)= 5x/x^2+1<BR>\n" );
document.write( "can someone explain this to me. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67057 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=67057\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the horizontal and vertical asymptotes of the following. Type none if the function does not have an asymptote.<BR>\n" );
document.write( "a. <BR>\n" );
document.write( "f(x) = 2x + 3/x + 3 <BR>\n" );
document.write( "Vertical asymptote where denominator = 0 ; x+3=0 when x=-3<BR>\n" );
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document.write( "Horizontal asymptote where y=2/1 = 2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%282x%2B3%29%2F%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%282x%2B3%29%2F%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "g(x)= 5x/x^2+1<BR>\n" );
document.write( "Vertical asymptote ? None because x^2+1 is always positive.<BR>\n" );
document.write( "Horizontal asymptote where y= 0x^2/1x^2 = 0/1 = 0<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C5x%2F%28x%5E2%2B1%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C5x%2F%28x%5E2%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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