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

Jan 29, 2016

Vertical asymptote at $x = \ln 2$.
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 ${e}^{x} = 2$ $\implies x = \ln 2$.

Horizontal asymptotes occur at $y = {\lim}_{x \to \pm \infty} \left[\frac{4 {e}^{x}}{{e}^{x} - 2}\right] = 4$

The graph of the function verifies this.

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