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5-2 Relations Objective: To identify the domain, range, and inverse of a function and to show relations as sets of ordered pairs, tables, mappings, and graphs. Drill #57 Graph the following points. Then state what quadrant they are in: 1. A ( 4, 5 ) 2. B ( -3, 2 ) 3. C ( -1.5, - 4 ) 4. D ( 0, -5 ) 5. E ( -5, 0 ) 6. F ( 3.5, -2.5 ) Biology Page 262. There are 1.4 million classified species of microorganisms, invertebrates, plants, fish, … Relations ** Relations are a set of ordered pairs. (10.) Domain: The set of all the x- coordinates of a relation (11.) Range: The set of all the y- coordinates of a relation 4 ways to represent relations 1. 2. 3. 4. Set of ordered pairs Table Graph Mapping (12.) Mapping ** Definition: A mapping pairs each element in the domain with an element in the range. Example: { (1,4), (2, 2), (3, 1), (4, 3) } X Y x y 1 1 3 2 3 2 2 3 2 3 1 4 1 4 3 Table Mapping Guided Practice #57 Represent the following relation as a table, a mapping, and a graph: { (2, 3) , (2, -1) , ( 4, -1 ), (3, 3) } x y X Y ? ? Guided Practice Represent the relation from Drill #61 as a mapping: x -3 -1 1 1 3 4 y 3 2 1 3 -2 -2 X -3 -1 1 3 4 Y 3 2 1 -2 (13.) Inverse Definition: Relation Q is the inverse of relation S if and only if for every ordered pair (a,b) in S there is an ordered pair (b,a) in Q. To find the inverse of a relation for each ordered pair swap x and y values. Inverse The inverse of a relation can be obtained by switching the coordinates in each ordered pair. Example: Relation: Inverse: {(1,4),(-3,2),(7,-9)} {(4,1),(2,-3),(-9,7)} x y x y swap x and y 1 4 4 1 -3 2 2 -3 7 -9 -9 7 Find the Inverse Write the inverse of the following relation as a set of ordered pairs: x y -1.5 3 1 4 4 -1 5 2 6 -1.5 First make a table 1. Swap the x and y values Inverse x y x y -1.5 3 3 -1.5 1 4 4 1 -1 4 2 5 -1.5 6 4 -1 5 2 6 -1.5 2. Write as a set of ordered pairs: {(3,-1.5),(4,1),(-1,4), (-1,4),(2,5),(-1.5,6)} Classwork Complete 5-2 Study Guide Worksheet Homework complete section 5-2 (unit outline) Read Section 5-3 Equations as Relations