Function: Definition

1. 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.

2. 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".

3. 17 5 0 2 - 2 - 4 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.

4. 17 5 0 2 - 2 - 4 Function: Mapping Diagram Representation Here, the left oval represents the domain. The right oval represents the range. The rules that govern the correspondence between the two sets are: 1. Multiply the domain value by three. 2. Add two to the result.

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

6. 17 5 0 2 - 2 - 4 Function: Table Representations xy - 2 - 4 Here is the same function represented by a table of values: 0 2 5 17

7. 17 5 0 2 - 2 - 4 Function: Equation 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 orf (x) = 3x + 2.

8. 17 5 0 2 - 2 - 4 Function: Graph Representations Here is the same function represented by a graph (orange line pictured).

9. Function END OF PRESENTATION