Question

Select all representations for the domain of a function given by the number of hours slept in one day.
A. (24, ∞)
B. {x | x > 24}
C. [0, 24]
D. [0, ∞]
E. (0, 24)
F. {x | 0 ≤ x ≤ 24}
G. {x | x E R}

Answer 1

To determine the domain of a function representing the number of hours slept in one day, we need to consider the realistic limits on the amount of sleep a person can have in a given day. The maximum possible sleep hours in a day is 24, while the minimum is 0. Therefore, the suitable representation for the domain of such a function would include all numbers from 0 to 24, inclusive.

We can evaluate the given options:

- **A. (24, ∞)**: This represents values greater than 24, which is not possible for sleep duration. **Not suitable.**
- **B. {x | x > 24}**: This set includes only values greater than 24. **Not suitable.**
- **C. [0, 24]**: This includes all values from 0 to 24, inclusive. **Suitable.**
- **D. [0, ∞)**: This includes all non-negative values, which is not appropriate since hours cannot exceed 24 in a day. **Not suitable.**
- **E. (0, 24)**: This includes values from greater than 0 to less than 24, excluding both endpoints. **Not suitable.**
- **F. {x | 0 ≤ x ≤ 24}**: This set includes all values from 0 to 24, inclusive. **Suitable.**
- **G. {x | x E R}**: This represents all real numbers, which is not appropriate as sleep hours are constrained to a specific range. **Not suitable.**

The suitable representations for the domain of the function given by the number of hours slept in one day are:
- **C. [0, 24]**
- **F. {x | 0 ≤ x ≤ 24}**