Question

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

Answer 1

Horizontal asymptotes : `y = 1 rarr and y = 0 larr`. See the asymptotes-inclusive Socratic graph.

Explanation:

As `x to oo, e^x/(1+e^x)=1/(1+e^(-x)) to 1` and

as `x to -oo, it to0.`

y-intercept ( x = 0 ) : 1/2

graph{(e^x/(1+e^x)-y)(y-1.1)(y+.01)=0 [-10, 10, -5, 5]}