Answer
Graph II
Work Step by Step
The first graph contains the point $(1, 2)$ while the second graph contains $(3, 0)$.
To know which graph represents the given function, evaluate $f(x)$ when x = 1 and when x = 3.
When x = 1,
$f(1) = \ln{(1-2)} = \ln{(-1)}; \text{ this is undefined as $x$ cannot be negative}$
When x = 3,
$f(3) = \ln{(3-2)} = \ln{1} = 0$
The point is $(3, 0)$.
Graph II contains the point $(3, 0)$ but Graph I does not contain $(3, 0)$.
Therefore, the graph of the given function must be Graph II.