What is the horizontal asymptote of y=e^x ?

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The absolute asymptote of ##y=e^x## is ##y=0##.

The graph of ##y=e^x## is asymptotic to the indirect x-axis barely. Absolute asymptotes of a graph are akin to the end deportment of a business. Since

##lim_(x->-oo)e^x=0##

the absolute asymptote is ##y=0##.

This is consequently, for indirect values of x,

##e^x=1/(e^|x|##

And, as ##x->-oo##, ##1/e^|x|## gain advent nothing.

See effigy under for a graphical solution.

Notice that,

##lim_(x->oo)e^x=oo##

So, as increases outside spring, so does y.

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