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}