1. Copyright © 2007 Pearson Education, Inc. Slide 1-1

2. Copyright © 2007 Pearson Education, Inc. Slide 1-2 Chapter 1:Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions 1.3 Linear Functions 1.4 Equations of Lines and Linear Models 1.5 Linear Equations and Inequalities 1.6 Applications of Linear Functions

3. Copyright © 2007 Pearson Education, Inc. Slide 1-3 1.2 Introduction to Relations and Functions Two Types of Notation: 1.Set Builder Notation -{x | x > –2} is read “The set of all x such that x is greater than –2” 2.Interval Notation - (–2,  ) represents the set of all numbers greater than –2 Note that “(“ indicates that –2 is not included and a parenthesis is always next to the infinity symbol .

4. Copyright © 2007 Pearson Education, Inc. Slide 1-4 1.2 Interval Notation Example of Set-BuilderCorrespondingCorresponding Type of IntervalNotationInterval NotationGraph

5. Copyright © 2007 Pearson Education, Inc. Slide 1-5 1.2 Definitions: Relation, Domain, and Range 1.A set of ordered pairs is called a relation. 2.If we denote the ordered pairs of a relation by (x,y), -the set of all x-values is called the domain, and -the set of all y-values is called the range.

6. Copyright © 2007 Pearson Education, Inc. Slide 1-6 1.2 Example of a Relation Let F be a relation where F = {(1, 2),(–2, 5),(3, –1 )}. Then the Domain = {1, –2, 3} and the Range = {2, 5, – 1}. –The graph of F looks like the following:

7. Copyright © 2007 Pearson Education, Inc. Slide 1-7 1.2 Diagram of a Relation Relation F can be illustrated with a diagram. An arrow from 1 to 2 indicates that the ordered pair (1,2) belongs to F. -2 1 3 5 2 F

8. Copyright © 2007 Pearson Education, Inc. Slide 1-8 1.2 Graph of a Relation A graph of a line or curve in the xy-plane represents a relation. Let F represent a relation consisting of all ordered pairs having the form (x,2x), where x is a real number. Example: (-2,-4),(-1,-2),(0,0),(1,2),(2,4) (-2,-4)

9. Copyright © 2007 Pearson Education, Inc. Slide 1-9 1.2 Domain and Range from a Graph Domain Range Domain

10. Copyright © 2007 Pearson Education, Inc. Slide 1-10 1.2 Definition of a Function Function A function is a relation in which each element in the domain corresponds to exactly one element in the range. If x represents any element in the domain, then x is called the independent variable. If y represents any element in the range, then y is called the dependent variable. Examples Indicate whether the following relations are functions. 1.{(1,1),(1,2),(1,3),(2,4)} 2. x-5-4-3-201 y2222222 Yes, since each element in the domain corresponds to exactly one element in the range.

11. Copyright © 2007 Pearson Education, Inc. Slide 1-11 1.2 Test for Functions Vertical Line Test – If every vertical line intersects a graph in no more than one point, the graph is the graph of a function. This graph is of a function.This graph is not of a function.