The horizontal asymptote of ##y=e^x## is ##y=0##.
The graph of ##y=e^x## is asymptotic to the negative x-axis only. Horizontal asymptotes of a graph are related to the end behavior of a function. Since
##lim_(x->-oo)e^x=0##
the horizontal asymptote is ##y=0##.
This is because, for negative values of x,
##e^x=1/(e^|x|##
And, as ##x->-oo##, ##1/e^|x|## will approach zero.
See image below for a graphical interpretation.
Notice that,
##lim_(x->oo)e^x=oo##
So, as increases without bound, so does y.
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Get The Answer What is the horizontal asymptote of ##y=e^x## ?
The horizontal asymptote of ##y=e^x## is ##y=0##.
The graph of ##y=e^x## is asymptotic to the negative x-axis only. Horizontal asymptotes of a graph are related to the end behavior of a function. Since
##lim_(x->-oo)e^x=0##
the horizontal asymptote is ##y=0##.
This is because, for negative values of x,
##e^x=1/(e^|x|##
And, as ##x->-oo##, ##1/e^|x|## will approach zero.
See image below for a graphical interpretation.
Notice that,
##lim_(x->oo)e^x=oo##
So, as increases without bound, so does y.
Previous answers to this question
This is a preview of an assignment submitted on our website by a student. If you need help with this question or any assignment help, click on the order button below and get started. We guarantee authentic, quality, 100% plagiarism free work or your money back.
Get The Answer