Interval notation is a way to represent a set of real numbers using brackets and parentheses. It is often used to represent the domain and range of a function. In interval notation, the following symbols are used:
- An open interval is represented by using parentheses ( )
- A closed interval is represented by using brackets [ ]
- An interval that includes one endpoint but not the other is represented by using a combination of parentheses and brackets, such as [ ) or ( ]
- Infinity is represented by using the symbols ∞ (positive infinity) and -∞ (negative infinity)
Here are some examples of interval notation for the domain and range of different functions:
Function f(x) = x^2 - 3x + 2
Domain: All real numbers (-∞, ∞)
Range: [3/4, ∞)
Function g(x) = 1/(x - 2)
Domain: (-∞, 2) U (2, ∞)
Range: (-∞, 0) U (0, ∞)
Function h(x) = √(4 - x^2)
Domain: [-2, 2]
Range: [0, 2]
Function j(x) = 2x - 5 for x ≤ 4, and j(x) = x^2 - 1 for x > 4
Domain: (-∞, 4] U (4, ∞)
Range: (-∞, -9] U [3, ∞)
In each of these examples, the domain and range are represented using interval notation. Remember that interval notation is a shorthand way to represent sets of real numbers, and it is useful for expressing the domain and range of a function in a compact and clear way.
