# What are the asymptotes and removable discontinuities, if any, of #f(x)= 2/( e^(-6x) -4) #?

##### 1 Answer

May 20, 2017

No removable discontinuities.

Asymptote:

#### Explanation:

Removable discontinuities are when

That leaves us finding the asymptotes (where the denominator = 0).

We can set the denominator equal to 0 and solve for

#e^(-6x)-4=0#

#e^(-6x)=4#

#-6x = ln4#

#x = -ln4/6 = -0.231#

So the asymptote is at

graph{2/(e^(-6x)-4) [-2.93, 2.693, -1.496, 1.316]}