# How do you find the domain, x intercept and vertical asymptotes of f(x)=lnx+2?

Feb 20, 2018

The $\ln x$-function only accepts positive values of $x$

#### Explanation:

There is no upper limit to $x$ so the domain is:
$0 < x < \infty$

As $x$ gets smaller the value of $\ln x$ gets more and more negative, or in 'the language':

${\lim}_{x \to 0} \ln x = - \infty$

Meaning $x = 0$ is the (only) vertical asymptote

The $x -$intercept is when $\ln x + 2 = 0 \to \ln x = - 2$
This means that $x = {e}^{- 2} \approx 0.135 \ldots$

The range of the function is from $- \infty$ to $+ \infty$

graph{ln x+2 [-7.78, 8.026, -3.534, 4.37]}