The idea of a function as a rule is usually expressed by some formula or mathmatical expression in terms of 2 or more variables. Suppose a formula expresses the variable y in terms of the variable x. Then we say that y is a function of x. For example, consider y = 3x + 1. For each value of x, this formula determines the corresponding value of y. Let x = 2, then y = 3(2) + 1 = 7. This means 7 is the value of the function at x = 2. Functions are usually denoted by a letter, typically f, written y = f(x) and read "y equals f of x." This notation means that the value of y is determined by the value of x using the function f. x is called the independent variable, and y the dependent variable since its value depends on the value of x. One definition of the function as a rule is: A function is a rule that assigns to each member in one set (the domain) exactly one member from another set (the range).
