Consider the functions.f(x) = (x + 1)2 – 4g(x) = –4 |x + 1|

For f(x) = (x + 1)² − 4, the squared term is at least 0, so f(x) is at least −4; its range is y ≥ −4. For g(x) = −4|x + 1|, the absolute value is at least 0, so multiplying by −4 makes g(x) at most 0; its range is y ≤ 0. Both functions can therefore take values from −4 through 0, so choice D is correct.

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