Which characteristic defines a one-to-one function?

A one-to-one function is defined by the principle that each value of x corresponds to exactly one value of y. This means that for every input (x), there is a unique output (y), and no two different inputs can produce the same output. This characteristic ensures that the function is predictable and consistent when mapping between the two sets.

In a one-to-one function, if you were to reverse the function, each value of y would lead back to one and only one value of x, reinforcing the uniqueness associated with the pairs involved. This feature is critical in many areas of mathematics, particularly in algebra and calculus, where understanding the behavior of functions is necessary for graph analysis, solving equations, and understanding relationships between variables.

The other options describe scenarios that do not align with the definition of a one-to-one function. For instance, if a value of x corresponds to multiple values of y, or if a value of y has multiple corresponding values of x, this would indicate a many-to-one relationship rather than a one-to-one relationship. Lastly, having no restrictions on x and y values does not clarify the unique mapping required for a one-to-one function, as it does not specify the relationship between each pair of values. This highlights the importance