f(x) = (x + 1)2 – 4 g(x) = –4 |x + 1| Which statement compares the ranges of the functions? 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.

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.

Step-by-step explanation:

From Function theory we get that range of a function is the set of values of so that exist a respective value of , whose set is the domain of the function. Let be and , the ranges of each function are, respectively:

f(x):

From Real Algebra we know that the square of every number is a non-negative number, which means that:

(Compatibility with addition)

(Definition/Result)

The range of is:

g(x):

From Real Algebra we know that a absolute value leads to non-negative number, which means that:

(, if )

(Definition/Result)

The range of is:

If we compare each range, we came into the conclusion that:

.

Thus, correct answer is: 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.

where is the figure

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