How does a function relate to a set of ordered pairs?

📌 CONCEPT: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), where each input is related to exactly one output.

📐 RULE / FORMULA: For a relation to be a function, it must satisfy the condition that each input corresponds to exactly one output.

💡 WORKED EXAMPLE: Consider the function f(x) = 2x + 1. To create a set of ordered pairs that satisfy this function, we can choose values of x and calculate the corresponding values of f(x). For example, if x = 0, f(0) = 2(0) + 1 = 1, so the ordered pair (0, 1) satisfies the function. Similarly, we can find other ordered pairs such as (1, 3), (2, 5), (3, 7), and (4, 9).

⚠️ COMMON MISTAKE: Students often mistakenly think that a relation is a function if it has no repeated inputs, but this is not necessarily true. A relation can have repeated inputs as long as each input corresponds to exactly one output.