Final answer:
Both functions f(x) = 4-x and g(x) = -√(x-4) share a domain of [4, ∞) and both decrease over the interval (4, ∞), making option B the correct answer.
Step-by-step explanation:
The key features that the functions f(x) = 4-x and g(x) = -√(x-4) have in common can be established by analyzing their domains, ranges, and behavior over their respective intervals. For f(x), it is clear that the function is defined for all real numbers, which means that its domain is (-∞, ∞). However, since the question might have a typo regarding the domain, we reflect on g(x) and notice that it is only defined for x >= 4. This is because the square root function cannot operate on negative numbers without producing imaginary results. Consequently, the domain common to both is [4, ∞) since f(x) does not have any restriction on its domain, we take the domain restriction from g(x).
Considering the range, f(x) being a linear function with a negative slope will have a range of (-∞, ∞), but this is not the case for g(x) because the output of a square root function is always nonnegative, making its range [0, ∞). Thus the common range is then [0, ∞).
Finally, when we consider the behavior over the interval (4, ∞), f(x) always decreases as x increases because of the negative coefficient before x. The g(x) function, being proportional to the negative square root of (x-4), will also decrease as x increases. This shared property confirms that both functions decrease over the interval (4, ∞).
Based on the analysis above, the correct answer is B) Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).