Select all representations for the domain of a function given by the number of hours slept in one day.
Responses
[0, ∞)
[0, ∞)
{x| x>24}
{x| x>24}
(24, ∞)
(24, ∞)
(0, 24)
(0, 24)
[0, 24]
[0, 24]
{x | 0≤ x ≤24}
{x | 0≤ x ≤24}
{x| x∈R}
{x| x∈R}
To determine the representations for the domain of a function given by the number of hours slept in one day, we need to consider the possible range of values for the input variable (hours slept).
1. [0, ∞): This represents a closed interval from 0 to positive infinity, including 0 and all positive numbers. It means that the number of hours slept can be any non-negative value.
2. {x| x>24}: This represents a set notation where the variable x is greater than 24. It implies that the number of hours slept must be greater than 24.
3. (24, ∞): This represents an open interval from 24 to positive infinity, excluding 24 but including all positive numbers greater than 24. It means that the number of hours slept must be more than 24 but not exactly 24.
4. (0, 24): This represents an open interval from 0 to 24, excluding both 0 and 24. It implies that the number of hours slept must be between 0 and 24 but not including those values.
5. [0, 24]: This represents a closed interval from 0 to 24, including both 0 and 24. It implies that the number of hours slept can be any non-negative value up to 24.
6. {x | 0≤ x ≤24}: This represents a set notation where x is between 0 and 24, inclusive. It means that the number of hours slept must be between 0 and 24, including both 0 and 24.
Therefore, the correct representations for the domain of the function "number of hours slept in one day" are:
- [0, ∞)
- (0, 24)
- [0, 24]
- {x | 0≤ x ≤24}