Question

Select all representations for the domain of a function given by the number of hours slept in one day. (2 points)
Responses

(0, 24)
(0, 24)

[0, 24]
[0, 24]

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

(24, ∞)
(24, ∞)

{x| x∈R}
{x| x∈R}

{x | 0≤ x ≤24}
{x | 0≤ x ≤24}

[0, ∞)

Answer 1

To represent the domain of a function given by the number of hours slept in one day, we must consider that the number of hours slept can range from 0 hours (not sleeping at all) to 24 hours (the maximum possible sleeping hours in a day). Therefore, the valid representations for the domain are:

1. **[0, 24]** - This includes all values from 0 to 24, inclusive.
2. **{ x | 0 ≤ x ≤ 24 }** - This is a set-builder notation that specifies the same range as [0, 24].

The other options do not represent valid ranges for the number of hours one can sleep in a day:

- **(0, 24)** does not include 0 or 24, which are valid sleeping hours.
- **{x | x > 24}** and **(24, ∞)** both suggest hours greater than 24, which is not possible in a single day.
- **{x | x ∈ R}** includes all real numbers, which is too broad.
- **[0, ∞)** suggests that one could sleep indefinitely, which is not the case.

Thus, the correct representations for the domain of the function (number of hours slept in one day) are:

- **[0, 24]**
- **{ x | 0 ≤ x ≤ 24 }**