# What is the domain and range of y=ln(x-3)+1?

Feb 14, 2016

The domain is $x > 3$.

The range is any real number.

#### Explanation:

Because $\ln \left(x\right)$ only takes input for $x > 0$, $\ln \left(x - 3\right)$ only takes input for $x > 3$.

The following is a graph of $y = \ln \left(x - 3\right) + 1$

graph{ln(x-3)+1 [-10, 10, -5, 5]}

It ranges from $- \infty$ to $\infty$.