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

[0, 60]
[0, 60]

{x| x∈R}
{x| x∈R}

{x | 0≤ x ≤60}
{x | 0≤ x ≤60}

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

(60, ∞)
(60, ∞)

[0, ∞)
[0, ∞)

(0, 60)

Answer 1

The domain of the function representing the number of minutes spent studying for the test in the last hour is between 0 and 60 minutes, inclusive, since one cannot study for a negative amount of time and cannot study more than 60 minutes in the last hour.

The appropriate representations for this domain are:

1. **[0, 60]** - This means the number of minutes can be 0 up to and including 60.
2. **{x | 0 ≤ x ≤ 60}** - This is a set-builder notation representing the same range.

The following options do not represent the domain correctly:
- **{x | x ∈ R}** - This includes all real numbers, which is not correct.
- **{x | x > 60}** - This only includes values greater than 60, which is incorrect.
- **(60, ∞)** - This also includes values greater than 60 and is thus incorrect.
- **[0, ∞)** - This suggests the possibility of studying indefinitely beyond 60 minutes, which is incorrect.
- **(0, 60)** - This excludes 0 and 60, which is also incorrect.

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