Question

How do you find the asymptotes for `y = (4 e^x)/(e^x - 2)`?

Answer 1

Vertical asymptote at `x=ln2`.
Horizontal asymptote at `y=4`.

Explanation:

There exists vertical asymptotes at points that set the denominator to zero,
that is, when `e^x-2=0` or when `e^x=2` `=>x=ln2`.

Horizontal asymptotes occur at `y=lim_(x->+-oo)[(4e^x)/(e^x-2)]=4`

The graph of the function verifies this.

graph{(4e^x)/(e^x-2) [-10.59, 11.91, -4.14, 7.11]}