Select all representations for the domain of a function given by elevation in feet at or above sea level
- All positive real numbers
- All non-negative real numbers
The representations for the domain of a function given by elevation in feet at or above sea level can be:
1. Set notation: {x | x is a real number and x ≥ 0}
2. Interval notation: [0, ∞) or [0, +∞)
3. Inequality notation: x ≥ 0
These representations indicate that the domain consists of all real numbers that are equal to or greater than zero (since elevation cannot be negative).
To determine the representations for the domain of a function representing elevation in feet at or above sea level, we need to consider the range of possible values.
1. Verbal representation: The domain can be described as "all values of elevation that are at or above sea level." This representation emphasizes the requirement that the elevation must be equal to or greater than zero.
2. Interval notation: In interval notation, the domain can be represented as [0, ∞). The square bracket on the left indicates that zero is included, and the infinity symbol on the right indicates that the domain extends indefinitely in the positive direction.
3. Set-builder notation: In set notation, the domain can be represented as {x | x ≥ 0}. This notation states that the domain consists of all values of x for which x is greater than or equal to zero.
4. Inequality notation: The domain can also be represented using an inequality: x ≥ 0. This inequality indicates that x must be greater than or equal to zero to be within the domain.
These representations capture the idea that the function representing elevation at or above sea level must have a non-negative value for the independent variable, which is the elevation itself.