Can a function have multiple representations as a relation?

📌 CONCEPT: A function can have multiple representations as a relation if the relation satisfies the condition that every element in the domain has a unique image in the codomain.

📐 RULE / FORMULA: For a relation to represent a function, each element of the domain must be associated with a unique element of the codomain, i.e., a function is a special type of relation where f(x) = y is true for at most one value of y for each value of x.

💡 WORKED EXAMPLE: Consider the relation R = {(2, 3), (4, 3), (6, 5)} in the set A = {2, 3, 4, 6} and B = {3, 5}. To represent this relation as a function f: A → B, we can define f(2) = 3, f(4) = 3, and f(6) = 5. This function satisfies the condition that every element in the domain has a unique image in the codomain.

⚠️ COMMON MISTAKE: Students often incorrectly assume that a relation with multiple ordered pairs automatically represents a function, forgetting that each element in the domain must have a unique image in the codomain.