The domain of the piecewise function is (−∞, ∞).
What is the domain of the function?
The domain is the set of possible inputs of a function, to identify the domain we need to look at the horizontal axis of the graph, and see over which interval is the function graphed.
Here we can see a piecewise function, it has 3 segments, which are on the intervals:
x ≤ -2
-2 < x < 2
x ≥ 2
So it is graphed over all the real numbers, then the domain is the last option (−∞, ∞).