What is the specific name of a relation where every element of the domain is mapped to only one element in the range?

A relation where every element of the domain is associated with only one element in the range is specifically defined as a function. In mathematical terms, for any given value in the domain, there is a unique output in the range. This unique mapping ensures that no input corresponds to multiple outputs, which is a fundamental characteristic of functions.

The concept of a function is essential in various areas of mathematics because it describes a consistent relationship between sets of numbers or objects, allowing for predictable outcomes from given inputs. Functions adhere to strict rules, such as the well-defined association between elements of the domain and range.

Other terms like mapping, association, and correlation may describe relationships, but they do not conform to the strict definition of a function. For instance, "mapping" can be a broader term referring to any relationship between sets, while "association" doesn't imply uniqueness and may indicate a more general connection. Similarly, "correlation" generally refers to a statistical relationship between two variables that doesn't necessarily imply a direct one-to-one correspondence. Thus, the precise term that captures the essence of a relation where each input corresponds to one and only one output is indeed a function.