Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What type of mapping occurs in a one-to-one function?

1. Every element in the range maps to multiple domain elements

2. Only some domain elements map to range elements

3. Each element in domain maps to exactly one range element

4. None of the elements are mapped

The correct answer is: Each element in domain maps to exactly one range element

In a one-to-one function, each element in the domain maps to exactly one unique element in the range, and importantly, each element in the range is also associated with a unique domain element. This characteristic ensures that no two different elements in the domain share the same output in the range, which is fundamental to the definition of a one-to-one function. This unique pairings prevent any overlap, distinguishing these functions distinctly from many-to-one functions, where multiple domain elements can yield the same range element. Therefore, the key aspect of a one-to-one function is its strict adherence to unique mappings. This property is crucial in various mathematical applications, including calculations involving inverses, where the one-to-one nature allows for the existence of an inverse function.