# What are the asymptotes for f(x) = 3 + log(x+2)?

Jun 23, 2015

For one, the argument of a log-function must be positive.

#### Explanation:

This means $x > - 2$ and $x = 2$ is the corresponding (vertical) asymptote, because you can get as near to 2 as you want.
In "the language" we say:

${\lim}_{x \to 2 +} f \left(x\right) = - \infty$

There is no horizontal asymptote, as the log function will grow with $x$ getting larger, even though the growth is slow, or:

${\lim}_{x \to \infty} f \left(x\right) = + \infty$
graph{3+log(x+2) [-5.67, 14.33, -3.32, 6.68]}