lightbulb Key Concepts

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1. What is a Function?

A function is a relation from a set A to a set B such that every element in set A is mapped to exactly one element in set B.

2. Domain, Codomain, and Range

• Domain: The set of all possible inputs (set A).
• Codomain: The set of all potential outputs (set B).
• Range: The set of actual outputs produced by the function.

3. Types of Functions

• One-to-One (Injective): Each element of A maps to a unique element of B.
• Onto (Surjective): Every element of B has at least one pre-image in A.
• Identity Function: f(x) = x for all x.
• Constant Function: f(x) = c for all x.