The leftmost line segment has a domain of -4 ≤ x < -1, or [-4, 1).
The central line segment has a domain of -1 ≤ x ≤ 2, or [-1, 2].
The rightmost line segment has a domain of 2 < x ≤ 5, or (2, 5].
Overall, this function has a domain of
[-4, 1) U [-1, 2] U (2, 5]
(where U means "union" in the set-theoretic notion)
But this also simplifies to the interval [-4, 5].
These correspond to the first and last choices.