Which statement defines a function?

Which statement defines a function?

• A. A relation in which each element of the domain is paired with exactly one element of the range
• B. A relation where multiple domain elements map to the same range element
• C. A relation with no pairing for any domain element
• D. A relation that pairs each range element with exactly one domain element

Answer: (A)

In a function, every input must have exactly one output. The statement that each element of the domain is paired with exactly one element of the range expresses that rule directly, so it matches the defining idea of a function. If an input doesn’t get any output, or if the description maps outputs back to inputs in the reverse way, or if it suggests not every input has an output, those situations don’t fit the idea of a function. And it’s okay for different inputs to share the same output, as long as each input still has its own single output.

In a function, every input must have exactly one output. The statement that each element of the domain is paired with exactly one element of the range expresses that rule directly, so it matches the defining idea of a function. If an input doesn’t get any output, or if the description maps outputs back to inputs in the reverse way, or if it suggests not every input has an output, those situations don’t fit the idea of a function. And it’s okay for different inputs to share the same output, as long as each input still has its own single output.