a function is a correspondence relationship in mathematics, from the non-empty number set a to the real number set b. simply put, a changes with b, and a is a function of b. to be precise, suppose x is a non-empty set, y is a non-empty number set, and f is a correspondence rule. if for each x in the correspondence rule f is said to be a function on x, denoted as y=f(x), and value range (the value range is a subset of y), x is called the independent variable, and y is called the dependent variable. it is also customary to say that y is a function of x. correspondence rules and domain are two elements of a function.