document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=110934>Question 110934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> FIND THE EQUATIONS OF ANY HORIZONTAL ASYMPTOTES WITHOUT GRAPHING\r<BR>\n" );
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document.write( "Y=E^X-8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80907 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=80907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When x is a really large negative number (like -1,000,000) this means we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-1000000%29=1%2Fe%5E1000000 ALIGN=MIDDLE  ALT=\"e%5E%28-1000000%29=1%2Fe%5E1000000\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a really small number. If you keep going, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5Ex ALIGN=MIDDLE  ALT=\"e%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > will become small enough that will consider it to be zero. So the only thing left is the \"-8\". So the horizontal asymptote is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Notice if we graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=e%5Ex-8 ALIGN=MIDDLE  ALT=\"y=e%5Ex-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+exp%28x%29-8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+exp%28x%29-8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and we can see that the horizontal asymptote is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-8 ALIGN=MIDDLE  ALT=\"y=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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