Final answer:
The range of the function f(x) = -|x| - 3 is ((-∞, -3)).
Step-by-step explanation:
The absolute value function, f(x) = -|x| - 3, is a piecewise function that changes its behavior at a certain point. In this case, the function changes when x = 0. For x < 0, the expression -|x| - 3 gives negative values. And for x ≥ 0, the expression -|x| - 3 gives non-negative values.
Therefore, the range of the function f(x) is ((-∞, -3)). Option A. ((-∞, -3)) is the correct answer.