Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What does it mean if a function is one-to-one?

1. It has multiple outputs for one input

2. It passes the vertical line test only

3. Each input maps to a unique output

4. It can be expressed as a linear equation

The correct answer is: Each input maps to a unique output

A function is considered one-to-one if each input maps to a unique output. This means that for every distinct value in the domain (the set of all possible inputs), there is a corresponding distinct value in the range (the set of all possible outputs). No two different inputs can produce the same output. This property is crucial when determining the invertibility of a function, as only one-to-one functions can be successfully reversed to isolate the input. In the context of the other options, having multiple outputs for one input contradicts the definition of a function itself, as a function's defining characteristic is that each input must correspond to exactly one output. The vertical line test is used to determine whether a graph represents a function but does not specifically indicate whether that function is one-to-one; it only checks if any input corresponds to more than one output. Lastly, while many one-to-one functions can be expressed as linear equations, this is not a defining characteristic of one-to-one functions overall, as one-to-one functions can be non-linear as well.