How do you find the horizontal asymptote of f(x)=e^1/x?

1 Answer
Sean
Jan 25, 2018

Please see below.

Explanation:

.

Functions have horizontal asymptotes when the value of the function, i.e. the value of #f(x)=y# approaches a certain constant value as #x# approaches #oo# or #-oo#.

Let's plug #oo# and #-oo# in for #x# and see what happens:

#y=e^(1/x)#

#y=e^(1/oo)=e^0=1#

#y=e^(1/-oo)=e^0=1#

This means #y=1# is a horizontal asymptote as can be seen in the graph of the function below:

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