Question

How do you find the vertical, horizontal and slant asymptotes of: `f(x)= Ln(2-x)+5`?

Answer 1

vertical asymptote: `x = 2`
horizontal asymptote: none
slant asymptote: none

Explanation:

By definition: `ln(2-x) > 0`

therefore `2-x >0` or `-x > -2` or `x < 2`

`ln(0)` is undefined, which means when `x = 2` the function has a vertical asymptote at `x=2`

Since the function is not a rational function: `(N(x))/(D(x))` there are no horizontal or slant asymptotes.