Function: Definition A function is a correspondence from a first set, called the domain, to a second set, called the range, such that each element in the domain corresponds to exactly one element in the range. Domain elements are called inputs. Range elements are called outputs.

The independent variable, x, denotes a member of the domain and the dependent variable, y, denotes a member of the range. We say, "y is a function of x". Function: Definition In this course the members of each set are real numbers. For now, x will represent a real number from the domain and y or f (x) will represent a real number from the range.

Function: Mapping Diagram Representation A function may be represented using a set of ordered pairs (x, y), a table of values, an equation, a graph, and a mapping diagram. Here is an example of a function represented by a mapping diagram

The rules that govern the correspondence between the two sets are: 1. Multiply the domain value by three. 2. Add two to the result. Function: Mapping Diagram Representation Here, the left oval represents the domain. The right oval represents the range

Here is the same function represented by a set of ordered pairs: { (- 2, - 4), (0, 2), (5, 17) }. Function: Ordered Pairs

Function: Table Representations Here is the same function represented by a table of values: x y

Let’s say that the mapping is just a partial representation of infinitely many ordered pairs. Then here is the same function represented by an equation: y = 3x + 2 or f (x) = 3x + 2. Function: Equation

Function: Graph Representations Here is the same function represented by a graph (orange line pictured).

Function