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)(0, 60)(0, 60) {x | 0≤ x ≤60}{x | 0≤ x ≤60}{x | 0≤ x ≤60}{x | 0≤ x ≤60} [0, 60][0, 60][0, 60][0, 60] {x| x>60}{x| x>60}{x| x>60}{x| x>60} {x| x∈R}{x| x∈R}{x| x∈R}{x| x∈R} (60, ∞)(60, ∞)(60, ∞)(60, ∞) [0, ∞)

Answer 1

The domain of the function representing the number of minutes spent studying for a test in the last hour would be constrained within the limits of 0 to 60 minutes, since it is not possible to study a negative number of minutes or more than 60 minutes within the last hour.

The suitable representations for this domain are:

1. **(0, 60)** - This notation indicates an open interval, meaning it does not include 0 and 60. However, since the study time can be 0 or up to 60 minutes, this may not be the best representation.

2. **{x | 0 ≤ x ≤ 60}** - This set-builder notation correctly represents all \( x \) values that are between 0 and 60, inclusive.

3. **[0, 60]** - This interval notation represents all values from 0 to 60, including both endpoints, which accurately describes the valid range.

The other representations listed like {x| x>60}, {x| x∈R}, (60, ∞), and [0, ∞) are either too broad or not applicable to the situation given the constraints.

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

While (0, 60) might seem relevant at first glance, it would exclude important boundary values for this context. Therefore, the more precise representations are the set-builder notation and the interval notation that include both endpoints.