Select all representations for the domain of a function given by elevation (in feet) at or above sea level.
{x|x∈R}
start set x such that x is in the real numbers end set
{x|x≥0}
start set x such that x is greater than or equal to 0 end set
[0, ∞)
[0, ∞)
{x|x>0}
start set x such that x is greater than 0 end set
(0, ∞)
(0, ∞)
(−∞, ∞)
(−∞, ∞)
The correct representations for the domain of a function given by elevation (in feet) at or above sea level are:
(0, ∞)
(0, ∞)
These represent the set of all real numbers greater than zero.
To select all representations for the domain of a function given by elevation at or above sea level, we need to consider the possible values that x can take. In this case, we want x to represent elevation in feet at or above sea level, which means x should be non-negative.
Let's go through each representation and determine which ones meet this criterion:
1. {x|x∈R}: This notation indicates that x belongs to the set of all real numbers. Since we want x to be non-negative, this representation includes negative numbers as well. Therefore, this representation is not suitable.
2. {x|x≥0}: This representation specifies that x is greater than or equal to 0, which matches our requirement. It represents the set of non-negative real numbers.
3. [0, ∞): This interval notation is commonly used to represent a range that includes the lower bound (0) but extends indefinitely towards positive infinity. It also meets our requirement and encompasses the set of non-negative real numbers.
4. {x|x>0}: This notation represents x values that are greater than 0, excluding 0 itself. Since we want to include 0 (sea level) as well, this representation is not suitable.
5. (0, ∞): This interval notation represents a range that starts from a value greater than 0 (excluding 0) and extends indefinitely towards positive infinity. As mentioned before, we want to include 0 (sea level), so this representation is not suitable.
6. (−∞, ∞): This interval notation represents the entire set of real numbers, including negative and positive numbers. Since we want to limit x to non-negative values, this representation does not satisfy our requirement.
Based on the analysis, the representations that correctly represent the domain of the given function are:
- {x|x≥0}
- [0, ∞)