Which statement best defines a function?

Which statement best defines a function?

• A. A relation in which one quantity depends on the other, with each x-value having a unique y-value.
• B. A relation that lists all possible ordered pairs.
• C. Any relation between two variables without restrictions.
• D. A relation where y-values determine x-values.

Answer: (A)

A function is a relation where each input x is assigned exactly one output y. This means once you pick x, there is a single y that goes with it, not multiple possibilities. The statement that matches this describes a quantity that depends on the other, with each x-value having a unique y-value, which is precisely the defining idea of a function. General relations can pair many different y values with the same x, or miss outputs for some x. Simply listing all ordered pairs describes a relation, but doesn’t guarantee the single-y-for-each-x rule. Saying that y-values determine x-values describes an inverse idea, which isn’t the defining property of a function. So the statement that captures the essential idea is the one that enforces exactly one y for every x.

A function is a relation where each input x is assigned exactly one output y. This means once you pick x, there is a single y that goes with it, not multiple possibilities. The statement that matches this describes a quantity that depends on the other, with each x-value having a unique y-value, which is precisely the defining idea of a function.

General relations can pair many different y values with the same x, or miss outputs for some x. Simply listing all ordered pairs describes a relation, but doesn’t guarantee the single-y-for-each-x rule. Saying that y-values determine x-values describes an inverse idea, which isn’t the defining property of a function. So the statement that captures the essential idea is the one that enforces exactly one y for every x.