The function which describes the correspondence between two variables x and y which are obtained by the finite rules is called an algebraic function. For example f(x) = y = x + 2.
Algebraic functions include only algebraic operations like addition, subtraction, multiplication, and division, and fractional and rational exponents. An algebraic function is like a machine where some real numbers go in, a given set of mathematical operations occurs as a process and another number is returned out.
The number that goes in is called a domain generally denoted as x and the number that comes out is called a range generally represented as y. The process that occurs is the function. There are various types of algebraic functions such as linear, quadratic, cubic, polynomial, and radical.