Question

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

{x | 0≤ x ≤60}
{x | 0≤ x ≤60}

(60, ∞)
(60, ∞)

[0, 60]
[0, 60]

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

[0, ∞)
[0, ∞)

(0, 60)
(0, 60)

{x| x∈R}

Answer 1

The domain of the function, which is defined by the number of minutes spent studying for the test in the last hour, can be correctly represented by the following options:

1. **{x | 0 ≤ x ≤ 60}**: This representation indicates that x can take any value from 0 to 60, inclusive.

2. **[0, 60]**: This is another way of representing the same range of values, using interval notation to indicate that both endpoints (0 and 60) are included.

The other options are not correct because:

- **(60, ∞)** indicates values greater than 60, which is not applicable.
- **{x| x > 60}** indicates values greater than 60, which is not applicable.
- **[0, ∞)** indicates values starting at 0 and going to infinity, which is not applicable.
- **(0, 60)** indicates values between 0 and 60, excluding the endpoints, which is not correct for studying time that can include 0 and 60 minutes.
- **{x | x ∈ R}** indicates all real numbers, which is not applicable.

Therefore, the correct representations for the domain are:
- **{x | 0 ≤ x ≤ 60}**
- **[0, 60]**