Question

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

Answer 1

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

Explanation:

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.