A function is a rule, correspondence, or mapping that assigns to each real number (**the input**) in a certain set one and one real number (**the output**). The set is called the domain of the function, and is the **dependent variable**, since its value depends on the value of . Because can assign any value in the domain , we refer to as the **independent variable**. The set of values assumed by as runs through all values in is called the **range** of the function.

Most calculators have special keys for some of the more important functions such as and . The use of letters of the alphabet to designate functions is not restricted exclusively to calculating machines. Although any letters of the alphabet can be us designate functions, the letters , , and as well as , , and are most common. (Letters of the Greek alphabet are also used.) For instance, if we wish to d the square-root function by the letter , we write .

If is a function, it is customary to write the value of y that corresponds to as , read “ of ” In other words, is the output produced when function is applied to the input .

For instance, if is the square-root function, then , , etc, and in general, for any nonnegative value of x, . Note carefully that does not mean times .