Question

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

Answer 1

The domain is `x>3`.

The range is any real number.

Explanation:

Because `ln(x)` only takes input for `x>0`, `ln(x-3)` only takes input for `x>3`.

The following is a graph of `y=ln(x-3)+1`

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

It ranges from `-oo` to `oo`.