Bell - Ringer Review Plot the following coordinates: (2 , 6) , ( -4 , 2) , ( 3 , 0) , (1 , -5) , ( - 2, -4)

Relations and Functions Domain and Range not this range though

Learning Target I will be able to understand the concepts of relations and functions and be able to represent each by Tables, Graphing, and Mapping Diagrams.

Definitions for Relation, Domain, and Range Relation – correspondence between a first set of values (domain) and a second set of values (range). This is referred to as ordered Pairs (x , y) Domain all of the x-values Range  all of the y-values Relations can be expressed by Tables, Graphs, and Mapping Diagrams.

Relation – correspondence between a first set of values (domain) and a second set of values (range). ordered Pairs (x , y) In the scoring system of some track meets, first place is worth 5 points, second place is worth 3 points, third place is worth 2 points, and fourth place is worth 1 point. This relation as ordered pairs are : {(1,5), (2,3), (3,2), (4,1)} Domain {1, 2, 3, 4, } Range {5, 3, 2, 1} As a table x y Place Points 1 5 2 3 4

Relations – As a Graph {(1,5), (2,3), (3,2), (4,1)} Domain {1, 2, 3, 4} Range {5, 3, 2, 1}

Relations as a Mapping diagram {(1,5), (2,3), (3,2), (4,1)} Place Points Domain { 1, 2, 3, 4} Range { 5, 3, 2, 1} 1 2 3 4 5 3 2 1

Domain and range “We do” Give the domain and range of each relation. domain: range: Domain:{ Range :{ X Y 7 3 4 2 1 5 8 6 4 3 9 8 5 2

Domain and range –of Graph “we do” Give the domain and range of the following graph D: R:

Domain and Range: -- “you do” X Y 7 9 -8 12 6 -14 11 3 -7 4 Give the Domain and Range of each relation 8 -4 20 7 -9 1 2 4 11 8 10

Domain and Range – “you do” Give the domain and range of the following graph

Domain and Range – express other way “I do” Express the relation{(-2,4) , (3,3), (0,6) ,(-1,-4)} As a table, graph, and mapping diagram. as a graph As a table: x Y

Domain and range - “I Do” As a mapping diagram {(-2,4) , (3,3), (0,6) ,(-1,-4)}

We Do –express the relation as a table and mapping diagram {(-1 , 4) , (5 , -2) , (3 , 5) , (4 ,0)} x y

Express the relation as a graph – We Do {(-2,4) , (3,3), (0,6) ,(-1,-4)}

Relations expressed _ “you do” Express the relation as a table, graph, and mapping diagram {(4 , 0) , (-2 , 4) , (3 , -5) , (0 , -2)}

Function A function is a special type of relation that pairs each domain value with exactly one range value. field trip Give the domain and Range of the relation and determine whether it is a function? D:{75, 68, 125} R:{2, 3} Function? Yes, each Domain is paired with exactly on range value Students (x) buses (y) 75 2 68 125 3

Function Give the domain and range of the relation. Determine whether the relation is a function. D:{7, 9, 12, 15} R:{-7, -1, 0} Function? NO – the domain 7 is paired with -1 and 0 7 9 12 15 -7 -1

Function – “We Do” Give the domain and range of each relation and determine whether the relation is a function {(8 , 2), (-4 , 1) , (-6 , 2) , (1 , 9)} D:{ } R: { } Function?_____ D:{ } R:{ } Function? _______ 44 4 3 2 -5 -4 -3

determining whether a relation is a function by the graph You can determine whether a graphed relation is a function by a vertical line test. If you can draw a vertical line through anywhere on the graph, and it crosses the graph more than once …………It is NOT a function

Exit slip Express the relation as a table, graph and a mapping diagram. {(-2 , -4) , (-1 , -1) , (0 , 0) , (1 , -1) , (2 , -4)} Is this relation a function?