What is a function?

A function from a set X to a set Y is a rule of correspondence that assigns to each element x in X exactly one element y in Y. A function is usually denoted by a letter such as f, g, or h. The set X is called the domain of f. The set of corresponding elements y in the set Y is called the range of the function. The unique element y in the range that corresponds to a selected element x in the domain X is called the value of the function at x, or the image of x, and is written f(x). Since the value of y depends on the choice of x, y is called the dependent variable and x is called the independent variable. There are many types of functions such as linear, quadratic, piecewise-defined, combining and inverse functions. For example a linear function is f(x)=ax+b where a doesn't equal 0 and a and b are constants.