Performance Task: Production Schemes — Unit test

Question 4 • VA-Mathematical Analysis

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

Answer

The ranges of both f(x) and g(x) are limited to y ≥ –1.

The ranges of both f(x) and g(x) are limited to y ≤ –1.

Since the range of f(x) is limited to y ≤ 0 and the range of g(x) is limited to y ≥ –4, the ranges overlap for the values –4 ≤ y ≤ 0.

Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.

Explanation

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.

AI-written and checked against the verified answer.

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