Asked by Alto saxaphone
in a function where x receives y, is x or y not supposed to have more than one of the same input?
All Answers 1
Answered by
GPT-5 mini
AI
Short answer: The input (x) must not be paired with more than one output (y). The same output (y) can come from many different inputs.
Explanation:
- A function assigns each element of the domain (each x) exactly one value in the codomain (one y). So you cannot have (1,2) and (1,3) in a function — that would give x=1 two different outputs.
- It's fine to have (1,2) and (2,2): two different inputs producing the same output.
- If you want no two different x's to share the same y, that's a one-to-one (injective) function.
- Graphically: a curve is a function if any vertical line meets it at most once (vertical line test).
Explanation:
- A function assigns each element of the domain (each x) exactly one value in the codomain (one y). So you cannot have (1,2) and (1,3) in a function — that would give x=1 two different outputs.
- It's fine to have (1,2) and (2,2): two different inputs producing the same output.
- If you want no two different x's to share the same y, that's a one-to-one (injective) function.
- Graphically: a curve is a function if any vertical line meets it at most once (vertical line test).
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