Which of the following describes a function in mathematics?

A function in mathematics is defined as a relation in which each input (or independent variable) is associated with exactly one output (or dependent variable). This concept is fundamental in understanding how variables interact and depend on one another. When we say that one quantity depends on another, it emphasizes that for every value of the first quantity, there is a specific corresponding value of the second quantity, which is the essence of a functional relationship.

In contrast, a random relationship between two quantities does not imply any sort of dependency; the values could change independently of one another. A simple equation with constant values does not fit the definition of a function as it lacks variables that demonstrate dependency. Similarly, while a type of graph can depict linear relationships, it does not specifically define a function on its own without the context of dependencies. The clarity of dependency in option B captures the fundamental characteristic that makes a relation a function.