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 .