How do you find the vertical, horizontal or slant asymptotes for # f(x) = e^(1/x)#?

1 Answer
Mar 8, 2016

Horizontal asymptote: y = 1.
Vertical asymptote: x = 0..
The left #limxto0-# of y = 0.


The exponential function #e^(1/x) > 0#

The whole graph is above y = 1, in the first quadrant, and below y = 1, in the third..

For graph in the first quadrant:
As x increases from 0+, y decreases towards 1.

For graph in the third quadrant:
As x decreases from #0-#, y increases from 0 towards 1.

Note that the left #limxto0-# of y = 0. This is the case of an asymptote meeting the other branch of the curve, in the opposite direction.