Question
Select all representations for the domain of a function given by the number of hours slept in one day. (2 points) Responses {x| x∈R} {x| x∈R} {x | 0≤ x ≤24} {x | 0≤ x ≤24} {x| x>24} {x| x>24} [0, ∞) [0, ∞) (0, 24) (0, 24) (24, ∞) (24, ∞) [0, 24]
Answers
GPT-4o mini
To represent the domain of a function that describes the number of hours slept in one day, we need to consider the possible range of hours someone can realistically sleep.
1. The minimum number of hours would be 0 (no sleep), and the maximum would be 24 (a full day).
2. Sleep hours cannot exceed 24 or be negative.
Based on these considerations, the valid representations for the domain of the function would include:
- {x | 0 ≤ x ≤ 24}
- [0, 24]
The other options can be dismissed for the following reasons:
- {x| x∈R} includes all real numbers, which is not appropriate as hours slept must be between 0 and 24.
- {x| x>24} and (24, ∞) are invalid, as sleep cannot exceed 24 hours.
- [0, ∞) and (0, 24) are also invalid since they include values outside of the range of 0 to 24.
In conclusion, the valid representations for the domain of hours slept are:
- {x | 0 ≤ x ≤ 24}
- [0, 24]
1. The minimum number of hours would be 0 (no sleep), and the maximum would be 24 (a full day).
2. Sleep hours cannot exceed 24 or be negative.
Based on these considerations, the valid representations for the domain of the function would include:
- {x | 0 ≤ x ≤ 24}
- [0, 24]
The other options can be dismissed for the following reasons:
- {x| x∈R} includes all real numbers, which is not appropriate as hours slept must be between 0 and 24.
- {x| x>24} and (24, ∞) are invalid, as sleep cannot exceed 24 hours.
- [0, ∞) and (0, 24) are also invalid since they include values outside of the range of 0 to 24.
In conclusion, the valid representations for the domain of hours slept are:
- {x | 0 ≤ x ≤ 24}
- [0, 24]