document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001042>Question 1001042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Basic question. f(x) equals y because plugging in some value x into the function will give you what the corresponding y-value will be. And the y-value of a LINEAR FUNCTION will always be the same thing as its horizontal asymptote?\r<BR>\n" );
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document.write( "I know the function will output differently for a rational function, and then the rules change. but for something like lim x -> &#8734; where the function is f(x) = 5+e^(-x^2). By plugging in &#8734; into the function this will output the horizontal asymptote because the horizontal asymptote is the same as y-value. In this case y = 5 and that is the horizontal asymptote.\r<BR>\n" );
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document.write( "not sure if this is right or not.\r<BR>\n" );
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document.write( "Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618337 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52793)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=618337\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Below is the plot of the functions &nbsp;y1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"5+%2B+e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;(in red) &nbsp;and &nbsp;y2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;(in green) &nbsp;with the horizontal asymptote &nbsp;y = 5 &nbsp;(in blue).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+330%2C+330%2C+-3.5%2C+3.5%2C+-1.5%2C+8.5%2C%0D%0A++++++++++5+%2B+e%5E%28-x%5E2%29%2C%0D%0A++++++++++e%5E%28-x%5E2%29%2C+5%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<B>Figure</B>. Plots y1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"5+%2B+e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and y2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The function &nbsp;y2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;tends to zero at &nbsp;x ---> +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore, &nbsp;the function &nbsp;y1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2B+e%5E%28-x%5E2%29 ALIGN=MIDDLE  ALT=\"5+%2B+e%5E%28-x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;tends to &nbsp;5 at &nbsp;x ---> +/-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "y = 5 &nbsp;is the horizontal asymptote for the function &nbsp;y1.\r<BR>\n" );
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document.write( "Notice that the function &nbsp;y1 &nbsp;is not a rational function, &nbsp;as well as the function &nbsp;y2.\r<BR>\n" );
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