document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=115406>Question 115406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me solve this problem asap?<BR>\n" );
document.write( "1. Find the horizonal and vertical asymptotes of the following. Type \"none\" if the function does not have an asymptote.<BR>\n" );
document.write( "A.f(x)=2x-3/x^2+2<BR>\n" );
document.write( "answer____________<BR>\n" );
document.write( "Horizonal________<BR>\n" );
document.write( "Vertical:____________\r<BR>\n" );
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document.write( "B. g(x)= 5x/x-1<BR>\n" );
document.write( "   Answer__________<BR>\n" );
document.write( "   Horizonal:________<BR>\n" );
document.write( "   Vertical_______\r<BR>\n" );
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document.write( "Thank you dearly </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84009 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> By definition, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=asymptote+ ALIGN=MIDDLE  ALT=\"asymptote+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a straight line continually approaching but never meeting a curve, or a line whose distance to a given curve tends to zero. An asymptote may or may not intersect its associated curve. \r<BR>\n" );
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document.write( "1.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%282x-3%29%2F%28x%5E2%2B2%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%282x-3%29%2F%28x%5E2%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical ALIGN=MIDDLE  ALT=\"vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" > asymptotes come from the zeroes of the denominator, so we need to set the denominator equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=zero ALIGN=MIDDLE  ALT=\"zero\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2=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+=+-2 ALIGN=MIDDLE  ALT=\"x%5E2+=+-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+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=+-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28-2%29 ALIGN=MIDDLE  ALT=\"+sqrt%28-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+solution ALIGN=MIDDLE  ALT=\"+solution\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the denominator has no zeroes, then<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+there ALIGN=MIDDLE  ALT=\"+there\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+are ALIGN=MIDDLE  ALT=\"+are\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+no ALIGN=MIDDLE  ALT=\"+no\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+vertical+ ALIGN=MIDDLE  ALT=\"+vertical+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=asymptotes ALIGN=MIDDLE  ALT=\"asymptotes\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the domain is \"all x\".<BR>\n" );
document.write( "Since the degree is greater in the denominator than in the numerator, the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y-values ALIGN=MIDDLE  ALT=\"+y-values\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be dragged down to the<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x-axis ALIGN=MIDDLE  ALT=\"+x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=the+ ALIGN=MIDDLE  ALT=\"the+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=horizontal ALIGN=MIDDLE  ALT=\"horizontal\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+asymptote ALIGN=MIDDLE  ALT=\"+asymptote\"   DISABLED_style= \"max-width:90%; height:auto;\" > is therefore \"<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;\" >\". Since I have found a horizontal asymptote, I don't have to look for a slant asymptote. Then the full answer is:\r<BR>\n" );
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document.write( "domain:  all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "vertical asymptotes:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none+ ALIGN=MIDDLE  ALT=\"none+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "horizontal asymptote:  <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;\" > (the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-axis ALIGN=MIDDLE  ALT=\"x-axis\"   DISABLED_style= \"max-width:90%; height:auto;\" >) <BR>\n" );
document.write( "slant asymptote:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none ALIGN=MIDDLE  ALT=\"none\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=+5x%2F%28x-1%29+ ALIGN=MIDDLE  ALT=\"g%28x%29=+5x%2F%28x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical ALIGN=MIDDLE  ALT=\"vertical\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+asymptote ALIGN=MIDDLE  ALT=\"+asymptote\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+1 ALIGN=MIDDLE  ALT=\"+x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "set the denominator and set it equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"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-1=0 ALIGN=MIDDLE  ALT=\"x-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+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "a<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+horizontal+ ALIGN=MIDDLE  ALT=\"+horizontal+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=asymptote ALIGN=MIDDLE  ALT=\"asymptote\"   DISABLED_style= \"max-width:90%; height:auto;\" > for this is...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim+x ALIGN=MIDDLE  ALT=\"lim+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"+5x%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=lim+x ALIGN=MIDDLE  ALT=\"lim+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >...<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5x%2F%28x-1%29+ ALIGN=MIDDLE  ALT=\"+5x%2F%28x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > --><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5 ALIGN=MIDDLE  ALT=\"+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );