Answer:
Option D.
Step-by-step explanation:
Since only one option is correct, a good strategy to solve this kind of exercises is to test the validity of each option, and choose the one that is correct.
From the graph, we can see that we have a quadratic function for x < 1 (not including x = 1 since we have a hole there) and a linear function for x ≥ 1 (including x = 1).
Option A.
Since the piece that corresponds to the quadratic function is defined for x ≥ 1, this option is NOT CORRECT.
Option B.
Since the piece that corresponds to the quadratic function is defined for x > 1, this option is NOT CORRECT.
Option C.
Since the piece that corresponds to the quadratic function is defined for x ≤ 1 (including 1), this option is NOT CORRECT.
Option D.
Since the piece that corresponds to the quadratic function is defined for x < 1 (not including 1), and the linear function is defined for x ≥ 1. Then, the domain of each piece is correct. By replacing x-coordinate on each piece function, we can also check that the points (0,2) and (-2, 6) belong to the graph of x² + 2, and the points (1, 1) and (2,0) belongs to the graph of -x + 2. Then, this option is CORRECT.
