Select all representations for the domain of a function given by time passed since your last meal.
Responses
{x| x>0}
{x| x>0}
[0, ∞)
[0, ∞)
(0, ∞)
(0, ∞)
(−∞, ∞)
(−∞, ∞)
{x| x∈R}
{x| x∈R}
{x| x≥0}
{x| x≥0}
The correct representations for the domain of a function given by time passed since your last meal are:
{x| x>0}
[0, ∞)
(0, ∞)
{x| x∈R}
{x| x≥0}
To select all representations for the domain of a function given by time passed since your last meal, we need to determine what the possible values of time passed can be.
The domain represents the set of all possible input values for a function. In this case, the input values are the time passed since your last meal.
Given the options provided, let's analyze each representation and see if it accurately describes the domain.
1. {x | x > 0}: This representation states that the time passed must be greater than 0. It means that the time passed cannot be zero or negative.
2. [0, ∞): This representation indicates that the time passed can be any non-negative value, including zero. The symbol "[ ]" denotes a closed interval, meaning that the endpoints (0 and ∞) are included.
3. (0, ∞): This representation also allows any positive value but excludes zero. The symbol "( )" denotes an open interval, indicating that the endpoints (0 and ∞) are not included.
4. (−∞, ∞): This representation suggests that the domain includes all real numbers, both positive and negative. However, in the context of time passed since your last meal, negative values would not be meaningful.
5. {x | x ∈ R}: This representation states that the time passed can be any real number. It encompasses all possible values, including both positive and negative.
6. {x | x ≥ 0}: This representation means that the time passed must be greater than or equal to zero. It includes zero and all non-negative values.
From the given options, the correct representations for the domain of the function "time passed since your last meal" are:
- {x | x > 0}
- [0, ∞)
- (0, ∞)
- {x | x ≥ 0}
These representations accurately capture the possible values for the time passed since your last meal.