Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What describes a many-to-one relationship in functions?

Each input maps to one output
One output can correspond to multiple inputs
It fails the vertical line test
It is a linear function

The correct answer is: One output can correspond to multiple inputs

In the context of functions, a many-to-one relationship is characterized by the scenario where multiple inputs can produce the same output. This means that it is possible for two or more different values in the domain of the function to yield the same single value in the range. For example, consider the function f(x) = x^2. The values f(2) and f(-2) both equal 4. Here, two distinct inputs (2 and -2) correspond to the same output (4), thus illustrating a many-to-one relationship. In contrast, the first option describes a one-to-one relationship, where each input maps to a unique output, while the third option, related to the vertical line test, is used to determine if a relation is a function at all rather than describing the nature of the relationships within it. The fourth option about linear functions does not inherently imply a many-to-one relationship but describes a specific type of relationship that can be one-to-one or many-to-one, depending on the function's characteristics.