Select all representations
for the domain of a function given by elevation (in feet) at or above sea level.
(2 points)
O {*|* ≥ 0}
O [0, ∞)
O {xx > 0}
O (0, ∞)
O (-00, 00)
O {XX ER}
O [0, ∞) and O (0, ∞)
To determine the correct representation for the domain of a function given by elevation at or above sea level, we need to understand the meaning behind each representation.
1. {*|* ≥ 0}: This representation uses set notation and the symbol "*" to represent any real number. It also includes the condition "≥ 0" to indicate that the elevation must be greater than or equal to zero. This representation is indicating that any elevation value that is nonnegative is within the domain of the function.
2. [0, ∞): This representation uses interval notation to define a closed interval that starts from 0 and goes to positive infinity. The inclusion of 0 means that zero is included in the domain, and the absence of an upper bound indicates that any positive elevation is also included.
3. {xx > 0}: This representation uses set notation and the symbol "x" to represent any real number. The condition "x > 0" states that the elevation must be strictly greater than zero. This representation indicates that only positive elevations are allowed in the domain.
4. (0, ∞): This representation uses interval notation to define an open interval that starts from 0 (excluded) and goes to positive infinity. The absence of 0 indicates that zero is not considered in the domain, and any positive elevation is included.
5. (-∞, ∞): This representation uses interval notation to define the entire real number line as the domain. It includes all possible real numbers, both positive and negative, indicating that any elevation is allowed.
6. {XX ER}: This representation uses set notation and the symbols "XX ER" to represent any real number. It doesn't specify any conditions or restrictions, indicating that all real numbers are included in the domain.
Among these representations, the correct one for the domain of a function given by elevation at or above sea level is the option: [0, ∞). This notation indicates that the domain includes zero (since elevations at sea level are included) and all positive elevations.