elect all representations for the domain of a function given by elevation (in feet) at or above sea level.(2 points)
Responses
[0, ∞)
{x|x>0}
(0, ∞)
(−∞, ∞)
{x|x≥0}
{x|x∈R}
[0, ∞) or {x|x≥0}
The correct responses for the representations of the domain of a function given by elevation (in feet) at or above sea level are:
[0, ∞)
{x|x≥0}
To determine the domain of a function given by elevation at or above sea level, we need to consider the possible values that the input (in this case, elevation) can take. The domain represents the set of all possible input values for the function.
Looking at the provided options, we can analyze each one to see if it correctly represents the domain.
[0, ∞) represents the interval from 0 to positive infinity, including 0. This interval includes all values greater than or equal to 0, so it is a valid representation of the domain.
{x|x>0} represents the set of all x values greater than 0. In the context of elevation at or above sea level, this means that we are excluding the value 0 itself. This representation is also correct.
(0, ∞) represents the interval from 0 to positive infinity, excluding 0. This means that only values greater than 0 are included. Again, this correctly represents the domain.
(−∞, ∞) represents the interval from negative infinity to positive infinity, which includes all real numbers. In the context of elevation at or above sea level, this representation is too broad, as it includes negative values that do not correspond to elevations at or above sea level. Therefore, it is not a valid representation of the domain.
{x|x≥0} represents the set of all x values that are greater than or equal to 0. Since this includes all values greater than 0 as well as 0 itself, this is another correct representation of the domain.
{x|x∈R} represents the set of all x values that belong to the set of real numbers. This representation is also too broad, as it includes all real numbers, regardless of their relevance to elevations at or above sea level.
Therefore, the correct representations for the domain of the function are:
[0, ∞)
{x|x>0}
(0, ∞)
{x|x≥0}