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}

[0, ∞)
[0, ∞)

(0, 24)
(0, 24)

{x| x>24}
{x| x>24}

(24, ∞)
(24, ∞)

[0, 24]
[0, 24]

{x | 0≤ x ≤24}

Answer 1

For the domain of a function representing the number of hours slept in one day, the acceptable range of values would be between 0 and 24 hours, including both endpoints. Therefore, the correct representations for the domain are:

1. \([0, 24]\)
2. \({x | 0 \leq x \leq 24}\)

These representations indicate that the number of hours slept can be anywhere from 0 hours (including) to 24 hours (including).

The other options provided do not accurately represent the domain of this function:

- \({x| x \in R}\) represents all real numbers, which is not appropriate for hours of sleep.
- \((0, 24)\) represents hours strictly greater than 0 and less than 24, which excludes 0 and 24.
- \({x| x > 24}\) and \((24, \infty)\) represent hours greater than 24, which is not relevant for the context of sleeping hours in a day.
- \([0, \infty)\) would suggest an unbounded upper limit, which is also not applicable.

Therefore, the representations of the domain are:
- \([0, 24]\)
- \({x | 0 \leq x \leq 24}\)