PPT-Defn: A relation is a set of ordered pairs.

Domain The x values of the ordered pair Range The y values of the ordered pair 35 Introduction to Functions x y 1 3 2 5 4 6 1 4 3 3 x y 4 2 3 8 6 1 1 9 5 6 x. Defn:limx!af(x)=Lifforall0,thereexistsa0suchthat0jxajimpliesjf(x)LjShowlimx!12= Defn:limx!af(x)=Lifxclosetoaandxaimpliesf(x)isclosetoL.Defn:limx!a+f(x)=Lifxclosetoaandx SET IDENTITIES:. Let A, B, C be subsets of a universal set U. . . Idempotent . Laws. a. A . . A = A b. A . . A = A. . Commutative . Laws. a. A . . B = B . . A b. A . . Defn:IfXisstationarytheautocovariancefunctionofXisCX(h)=Cov(X0;Xh).Defn:IfXandYarejointlystationarythenthecross-covariancefunctionisCXY(h)=Cov(X0;Yh).NoticethatCX(h)=CX(h)andCXY(h)=CYX(h)forallhands Coordinate system. : used to locate points . also call the Coordinate plane. Origin. : is a (0,0) and is the point at which the number lines intersect. X-Axis. : the horizontal number line. Y-Axis. : the vertical number line. Relations . & Functions. After today’s lesson, you should be able to:. Explain the difference between a relation and a function. Identify whether a relation is a function. Identify the domain and range of a relation or a function. Objective:. To graph relations. To identify functions. Relations. A relation is a set of pairs of input and output values.. You can write a relation as a set of ordered pairs.. Graphing Relations. To graph relations, plot the points. . Properties. L Al-. zaid. Math1101. 1. The Binary Relation. DEFINITION 1. Let A and B be sets. A . binary relation . from A to B is a subset of . AxB. .. In other words, . a binary relation. Section 9.3. Representing Relations Using Matrices. A relation between finite sets can be represented using a zero-one matrix. . Suppose . R. is a relation from . A. = {. a. 1. , . a. 2. , …, . a. set of ordered . pairs. .. An age of . 10 years . would correspond to a weight of 31 kg. . An age . of 16 years would correspond to a weight of . 53 kg . and . so on. .. This . type of information represents a relation between . Presented By: Andrew F. Conn. Lecture #22: Relations and Representations. November 28. th. , 2016. Binary relations establish a relationship between elements of two sets. Definition: . Let . and . be two sets. A . A function maps each element in the domain to exactly 1 element in the range. . Concept 1. Example 1. Domain and Range. State the domain and range of the relation. Then determine whether the relation is a function. If it is a function, determine if it is . Section. . 2.2. Relations. In symbols . we have (. a. , . b. ) = . {. {. a. }, {. Objectives: Determine whether a relation is a function, identify the domain and range, evaluate functions. Relation:. A set of ordered pairs. Domain (D):. The first element in an ordered pair. (abscissa). B-1. Relations and Functions. ACT WARM-UP. Emily scored 145, 170, and 165 in 3 bowling games. What should she score on her next bowling game if she wants to have an average score of exactly 170 for the 4 games?.