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, ∞)
[0, ∞)
{x | 0≤ x ≤24}
{x | 0≤ x ≤24}
[0, 24]
[0, 24]
(24, ∞)
(24, ∞)
{x| x>24}
{x| x>24}
{x| x∈R}
Responses
(0, 24)
(0, 24)
[0, ∞)
[0, ∞)
{x | 0≤ x ≤24}
{x | 0≤ x ≤24}
[0, 24]
[0, 24]
(24, ∞)
(24, ∞)
{x| x>24}
{x| x>24}
{x| x∈R}
Answers
GPT-4o mini
The domain of the function given by the number of hours slept in one day is limited to the range of possible sleep hours, which is from 0 to 24 hours, inclusive. Therefore, the valid representations for this domain are:
1. **(0, 24)** - This represents hours slept in an open interval from 0 to 24, but it does not include 0 or 24.
2. **[0, ∞)** - This incorrectly includes hours greater than 24, so it is not valid.
3. **{x | 0 ≤ x ≤ 24}** - This set notation properly includes all values from 0 to 24 inclusive.
4. **[0, 24]** - This interval includes both 0 and 24, which is valid.
5. **(24, ∞)** - This incorrectly includes hours greater than 24, so it is not valid.
6. **{x | x > 24}** - This incorrectly considers hours greater than 24, so it is not valid.
7. **{x | x ∈ R}** - This includes all real numbers and is too broad, so it is not valid.
The correct representations for the domain of this function are:
- **{x | 0 ≤ x ≤ 24}**
- **[0, 24]**
While (0, 24) is also listed, it does not include the endpoints, which are relevant for this particular situation since sleeping 0 hours or 24 hours both count as valid scenarios. Thus, the best representations are **{x | 0 ≤ x ≤ 24}** and **[0, 24]**.
1. **(0, 24)** - This represents hours slept in an open interval from 0 to 24, but it does not include 0 or 24.
2. **[0, ∞)** - This incorrectly includes hours greater than 24, so it is not valid.
3. **{x | 0 ≤ x ≤ 24}** - This set notation properly includes all values from 0 to 24 inclusive.
4. **[0, 24]** - This interval includes both 0 and 24, which is valid.
5. **(24, ∞)** - This incorrectly includes hours greater than 24, so it is not valid.
6. **{x | x > 24}** - This incorrectly considers hours greater than 24, so it is not valid.
7. **{x | x ∈ R}** - This includes all real numbers and is too broad, so it is not valid.
The correct representations for the domain of this function are:
- **{x | 0 ≤ x ≤ 24}**
- **[0, 24]**
While (0, 24) is also listed, it does not include the endpoints, which are relevant for this particular situation since sleeping 0 hours or 24 hours both count as valid scenarios. Thus, the best representations are **{x | 0 ≤ x ≤ 24}** and **[0, 24]**.