Reflecting Relations?

📌 CONCEPT: A relation R is said to be a function if every element in the domain has a unique image in the co-domain.

📐 RULE / FORMULA: For a relation to be a function, it must satisfy the condition that for every x in the domain, there exists a unique y in the co-domain such that (x, y) is in the relation.

💡 WORKED EXAMPLE: Consider the function f(x) = 2x + 1. Let's check if the relation R = {(x, y) | y = f(x)} is a function. For x = 2, f(2) = 2*2 + 1 = 5. For x = 2, there exists a unique y = 5 in the co-domain such that (2, 5) is in R. Therefore, R is a function.

⚠️ COMMON MISTAKE: Students often confuse the concept of a relation being a function with the concept of an inverse relation. A relation can be a function and still not have an inverse relation if it is not one-to-one.