Question

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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

(0, 60)
(0, 60)

(60, ∞)
(60, ∞)

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

[0, 60]
[0, 60]

{x | 0≤ x ≤60}
{x | 0≤ x ≤60}

[0, ∞)
[0, ∞)

{x| x∈R}

Answer 1

To represent the domain of a function that describes the number of minutes spent studying for this assignment in the last hour, we need to consider the relevant range of values for the minutes spent studying.

1. **Time Spent in Minutes**: Since we are discussing the last hour, the number of minutes spent studying can range from 0 minutes to a maximum of 60 minutes. Therefore, we cannot have negative values or values exceeding 60.

The appropriate representations for the domain of this function are:

- **[0, 60]**: This notation indicates that the interval includes both endpoints (0 and 60), meaning the minutes can be exactly 0 or exactly 60.
- **{x | 0 ≤ x ≤ 60}**: This set builder notation also includes all values from 0 to 60, including the endpoints.

The other options do not accurately represent the constraints of the problem:
- **(0, 60)**: This is incorrect because it excludes 0 and 60.
- **(60, ∞)**: This is not relevant since we are not considering time spent greater than 60 minutes.
- **{x | x > 60}**: This is not applicable as values cannot exceed 60 minutes.
- **[0, ∞)**: This is incorrect as it includes values beyond 60 minutes.
- **{x | x ∈ R}**: This includes all real numbers, which is not the correct representation for this specific situation.

Thus, the correct choices for the domain are:

- **[0, 60]**
- **{x | 0 ≤ x ≤ 60}**