Select all representations for the domain of a function given by time passed since your last meal. Responses (0, ∞) (0, ∞) (−∞, ∞) (−∞, ∞) {x| x>0} {x| x>0} [0, ∞) [0, ∞) {x| x≥0} {x| x≥0} {x| x∈R}
{x| x≥0} {x| x∈R}
The correct representations for the domain of a function given by time passed since your last meal are:
{ x | x > 0 }
{ x | x ≥ 0 }
[ 0, ∞ )
To determine the correct representations for the domain of a function given by time passed since your last meal, we need to understand the concept of domain and consider the context of the function.
The domain of a function refers to the set of all possible input values (or independent variable values) for the function. In the given question, the function represents the time passed since your last meal. We need to consider what values are valid inputs in the context of time.
Looking at the provided responses:
(0, ∞) - This representation uses parentheses and denotes all values greater than zero. The absence of a negative infinity symbol indicates that negative time values are excluded. However, in the context of time passed since your last meal, negative values are not possible, as time cannot pass before your last meal.
(−∞, ∞) - This representation uses parentheses and indicates all real numbers. It includes both positive and negative values. However, as mentioned earlier, negative values for time passed since your last meal are not possible.
{x| x>0} - This representation uses set builder notation and indicates all values greater than zero. It explicitly excludes zero.
[0, ∞) - This representation uses square brackets to indicate inclusion and denotes all values greater than or equal to zero. It includes zero.
{x| x≥0} - This representation uses set builder notation and indicates all values greater than or equal to zero. It explicitly includes zero.
{x| x∈R} - This representation uses set builder notation and indicates all real numbers. It includes both positive and negative values.
From the provided responses, the correct representations for the domain of the given function are:
- [0, ∞): This includes zero and all positive values.
- {x| x≥0}: This includes zero and all values greater than or equal to zero.
Therefore, the correct answers are [0, ∞) and {x| x≥0}.