Which statement describes a many-to-one function?

Which statement describes a many-to-one function?

• A. Each output corresponds to exactly one input
• B. The inverse exists for every y-value in the range
• C. f(x) is a function but the inverse is not
• D. The function passes the horizontal line test in both directions

Answer: (C)

Many-to-one means different inputs can map to the same output. This keeps f as a valid function—each input still has one output—but it breaks invertibility: the same output comes from multiple inputs, so the inverse wouldn’t be a function (it wouldn’t assign exactly one input to each output). That’s why the statement “f(x) is a function but the inverse is not” best describes a many-to-one function. If every output could come from exactly one input, or if the inverse existed for every y-value, you’d have a one-to-one situation, which is invertible. The horizontal line test in both directions would also indicate one-to-one behavior, not many-to-one.

Many-to-one means different inputs can map to the same output. This keeps f as a valid function—each input still has one output—but it breaks invertibility: the same output comes from multiple inputs, so the inverse wouldn’t be a function (it wouldn’t assign exactly one input to each output).

That’s why the statement “f(x) is a function but the inverse is not” best describes a many-to-one function. If every output could come from exactly one input, or if the inverse existed for every y-value, you’d have a one-to-one situation, which is invertible. The horizontal line test in both directions would also indicate one-to-one behavior, not many-to-one.