Final answer:
The domain and range given in the question do not align perfectly with the actual domain [0, 20] and range {20} of the described function, but the closest given option would be B, albeit with incorrect range notation.
Step-by-step explanation:
The question is asking us to determine the domain and range of a function that seems to be poorly described in the question itself. However, by interpreting the question as to when x is the input for a function that translates -infinity, we will make a reasonable guess. Since it's impossible to have an infinity value within the domain or range in a real-world function, options C and D can be immediately disregarded because they suggest infinities are included within the domain and range.
Let's clarify what we do know. The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). The example provided for f(x) shows that x is limited from 0 to 20, hence the domain is between these two values.
For a function that is a horizontal line, such as f(x) = 20 (when 0 ≤ x ≤ 20), its range includes only the single value where the horizontal line exists, which is y = 20. So, in this case, the domain would be [0, 20] because x can take on any value within that interval, and the range would be {20} because there's only one possible output value.
Given the choices A through D and interpreting the function as a horizontal line over a restricted domain:
- Option A is incorrect because the range is not all real numbers but rather a single value.
- Option B appears to be the most appropriate as it correctly reflects the domain as all real numbers, but uses incorrect notation for the range, which in this particular case should only be {20}.
- Option C is incorrect due to including infinity in the domain and range.
- Option D is also incorrect for the same reason as C.
Hence, none of the provided options A-D correctly and completely reflect the domain and range of the given function, as they all incorrectly imply an infinite range, but the most appropriate response given the options, leaning in favor of standard real-number domain and range conventions, would be option B (Domain: (-infinity, infinity), Range: [-infinity, infinity]). However, it should be understood that the actual domain is [0, 20] and the range is {20}.