Which statement describes a many-to-one function?

Which statement describes a many-to-one function?

• A. Inverse is a function.
• B. Inverse is not a function.
• C. Each input maps to a unique output.
• D. The function is linear.

Answer: (B)

A many-to-one function sends several inputs to the same output, so you can’t uniquely determine the input from a given output. Because of that, the inverse relation would have more than one input for a single output, which means the inverse wouldn’t be a function. That’s why saying the inverse is not a function best describes a many-to-one function. The other ideas don’t capture the idea as precisely. A statement that every input has a unique output is true for any function, not just many-to-one. And being linear doesn’t necessarily describe many-to-one behavior—the common linear functions with nonzero slope are one-to-one, so they don’t describe the general case of many-to-one.

A many-to-one function sends several inputs to the same output, so you can’t uniquely determine the input from a given output. Because of that, the inverse relation would have more than one input for a single output, which means the inverse wouldn’t be a function. That’s why saying the inverse is not a function best describes a many-to-one function.

The other ideas don’t capture the idea as precisely. A statement that every input has a unique output is true for any function, not just many-to-one. And being linear doesn’t necessarily describe many-to-one behavior—the common linear functions with nonzero slope are one-to-one, so they don’t describe the general case of many-to-one.