Answer
please see image
Work Step by Step
1. Start by sketching $f_{1}(x)=\ln x$
2. $f_{2}(x)=f_{1}(x-2)=\ln(x-2)$
(shift $f_{1}, $2 units to the right)
3. $f(x)=f_{2}(x)+1=\ln(x-2)+1$
(shift $f_{2},$ 1 unit up)
Its domain is $x>2.$
(screenshot included)