1. Table of Contents 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 A function is a correspondence between two sets governed by some rule(s) such that each member of the first set corresponds to exactly one member of the second set. The first set is called the domain of the function. The second set is called the range of the function. 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.

2. Table of Contents Function: Mapping Diagram Representation Slide 2 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 in part, by a mapping diagram. 5 17 02 - 2- 4

3. Table of Contents 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 in part, the domain. The right oval represents in part, the range. Slide 3 5 17 02 - 2- 4

4. Table of Contents Here is the same function represented in part, by a set of ordered pairs: { (- 2, - 4), (0, 2), (5, 17) }. Function: Ordered Pairs, Table Representations Slide 4 5 17 02 - 2- 4 x y - 2 - 4 Here is the same function represented in part, by a table of values: 0 2 5 17

5. Table of Contents Here is the same function represented by an equation: y = 3x + 2 or f (x) = 3x + 2. Function: Equation, Graph Representations Slide 5 5 17 02 - 2- 4 Here is the same function represented by a graph (orange line pictured).

6. Table of Contents Function