Question

Select all representations for the domain of a function given by the number of minutes spent studying for this assignment in the last hour. (1 point)
Responses

{x| x∈R}
{x| x∈R}

(60, ∞)
(60, ∞)

[0, 60]
[0, 60]

[0, ∞)
[0, ∞)

{x | 0≤ x ≤60}
{x | 0≤ x ≤60}

{x| x>60}
{x| x>60}

(0, 60)

Answer 1

The domain of the function described is the number of minutes spent studying for the assignment in the last hour. Given that there are 60 minutes in an hour, the valid range of minutes spent studying must be between 0 and 60 minutes, inclusive. Therefore, the valid representations for the domain are:

1. **[0, 60]** - This indicates all values from 0 to 60, including both endpoints.
2. **[x | 0 ≤ x ≤ 60]** - This is another way of stating that x is between 0 and 60, inclusive.
3. **[0, ∞)** - This one is technically incorrect as it suggests studying can go beyond 60 minutes, which it cannot.
4. **(0, 60)** - This one is incorrect since it does not include 0 and 60.
5. **{x | x ∈ R}** - This one is incorrect because it includes all real numbers.
6. **(60, ∞)** - This is incorrect as it suggests studying can start from above 60 minutes.
7. **{x | x > 60}** - This is incorrect because it again suggests values greater than 60 minutes are permissible.

Consequently, the correct representations for the domain are:

- [0, 60]
- {x | 0 ≤ x ≤ 60}