What is the domain and range of f(x) = |x - 2|?

There are no constraints on the input to the function in the problem. $x$ is able to assume any value therefore the Domain is the set of All Real Numbers. Or: $\left\{\mathbb{R}\right\}$
Therefore, because this is an absolute value function of a linear transformation, the Range is the set of all Real numbers greater than or equal to $0$