select all representations for the domain of a function given by the number of hours slept in one day
- 0.5, 1, 1.5, 2, 2.5, ...
- 0, 1, 2, 3, 4, ...
- [0, ∞)
- {x ∈ ℝ | x ≥ 0}
- {x | x is a non-negative real number}
- (0, ∞)
To determine the representations for the domain of a function representing the number of hours slept in one day, we need to consider what values are reasonable or possible for the input of the function. Let's explore the different ways to represent the domain:
1. Inequality representation: We can represent the domain using inequalities if we have certain constraints on the number of hours slept. For example, if we assume the number of hours slept must be greater than or equal to 0, we can represent the domain as: 0 ≤ x, where x represents the number of hours slept.
2. Interval notation: If we want to represent the domain using interval notation, we can use square brackets to indicate that the boundary values are included. Since the number of hours slept cannot be negative, the domain can be written as: [0, ∞), where ∞ represents infinity.
3. Set notation: Another way to represent the domain is using set notation. We can express the domain as a set of all real numbers greater than or equal to 0: {x | x ≥ 0}.
4. Graphical representation: If you are familiar with graphing, you can also represent the domain on a number line. Starting from 0 and moving towards positive infinity, the domain includes all values on or to the right of 0.
In summary, the representations for the domain of a function representing the number of hours slept in one day can be: 0 ≤ x, [0, ∞), {x | x ≥ 0}, or a number line starting from 0 towards positive infinity.