Let max $\{a, b\}$ denote the maximum of two real numbers $a$ and $b$. Which of the following statement(s) is/are $\text{TRUE}$ about the function $f(x) = \text{max}\{3 - x,x -1\}$?

- It is continuous on its domain.
- It has a local minimum at $x = 2$.
- It has a local maximum at $x = 2$.
- It is differentiable on its domain.