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

Feb 22, 2017

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

#### Explanation:

By definition: $\ln \left(2 - x\right) > 0$

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

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

Since the function is not a rational function: $\frac{N \left(x\right)}{D \left(x\right)}$ there are no horizontal or slant asymptotes.