# How do you find the domain and range of  ln(x - 3) + 2?

Oct 14, 2017

Since the $\ln$ function is only defined for positive arguments, the domain is $x > 3$ with no upper limit, or in other words $3 < x < \infty$.

#### Explanation:

The $\ln$ function can reach any value from $- \infty \to + \infty$ (even if it rises very slowly), which will not change is we add $2$. So this is the range .
graph{ln(x-3)+2 [-37.34, 55.15, -23.9, 22.35]}