Relations / Functions
Least You Need to Know: Functions
A function gives exactly one output for each input in its domain. The key is checking repeated inputs carefully.
Least you need to know
- A function cannot assign two different outputs to the same input.
- Different inputs are allowed to share the same output.
- The domain is the set of allowed inputs.
- One-to-one is stronger than being a function.
Key notation
- f: A → B — function from A to B
- f(x) — output at x
- domain — allowed inputs
Worked example
- Set of pairs: {(1,4),(2,4),(3,5)}.
- This is a function because each input 1, 2, and 3 has exactly one output.
- It is not one-to-one because both 1 and 2 map to 4.
Common mistakes
- Students often think repeated outputs break the function rule.
- Students often forget that the problem is about inputs, not outputs.
- Students often confuse 'function' with 'one-to-one function'.
How to recognize it
- If one input points to two outputs, it is not a function.
- Repeated outputs are allowed unless the question asks about one-to-one.
- On arrow diagrams, scan left-side nodes first.
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