what is a math function
A function ƒ from a set D to a set Y is a rule that assigns a unique (single) element ƒ(x)∊Y to each element x∊D.
what is a function domain
A domain is the set of all possible input values (x-values) for which a function is defined and produces a valid output. It answers the question “What values can I put into this function?”
For example:
- For f(x) = x², the domain is all real numbers since you can square any real number
- For f(x) = 1/x, the domain is all real numbers except x = 0 (since division by zero is undefined)
- For f(x) = √x, the domain is x ≥ 0 (since you can’t take the square root of negative numbers in the real number system)
what is a function range
A range is the set of all possible output values (y-values) that a function can produce. It answers the question “What values can this function actually output?”
For example:
- For f(x) = x², the range is y ≥ 0 (since squaring any real number gives a non-negative result)
- For f(x) = sin(x), the range is -1 ≤ y ≤ 1 (sine oscillates between these bounds)
- For f(x) = 2x + 3, the range is all real numbers (this linear function can produce any y-value)
what is a function codomain
A codomain is the set of all possible values that a function is declared to map to - it’s the “target space” where the function’s outputs are supposed to land.
The key distinction is:
- Codomain: The set you say the function maps to (declared beforehand)
- Range: The set the function actually maps to (determined by the function’s behavior) The range is always a subset of (or equal to) the codomain.
Think of it this way: domain is what goes in, range is what comes out. The domain constrains your inputs, while the range describes all the possible outputs you can get from those valid inputs.
