Function Definition A function is a correspondence from

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Function: Definition • A function is a correspondence from a first set, called the

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.

Function: Definition In this course the members of each set are real numbers. For

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. 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: Mapping Diagram Representation A function may be represented using a set of ordered

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. 17 5 0 -2 2 -4

Function: Mapping Diagram Representation Here, the left oval represents the domain. The right oval

Function: Mapping Diagram Representation Here, the left oval represents the domain. The right oval represents the range. 17 5 0 -2 2 -4 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: Ordered Pairs 17 5 0 -2 2 -4 Here is the same function

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

Function: Table Representations 17 5 0 -2 Here is the same function represented by

Function: Table Representations 17 5 0 -2 Here is the same function represented by a table of values: 2 -4 x y -2 -4 0 25 17

Function: Equation 17 5 0 -2 2 -4 Let’s say that the mapping is

Function: Equation 17 5 0 -2 2 -4 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 = 3 x + 2 or f (x) = 3 x + 2.

Function: Graph Representations 17 5 0 -2 Here is the same function represented by

Function: Graph Representations 17 5 0 -2 Here is the same function represented by a graph (orange line pictured). 2 -4

Function

Function

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