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5-2 Relations

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 )

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5-2 Relations

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  1. 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.

  2. 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 )

  3. Biology Page 262. There are 1.4 million classified species of microorganisms, invertebrates, plants, fish, …

  4. 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

  5. 4 ways to represent relations • Set of ordered pairs • Table • Graph • Mapping

  6. (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) } XY 1 2 3 3 2 4 1 Table Mapping

  7. 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 ? ?

  8. Guided Practice Represent the relation from Drill #61 as a mapping: X Y -3 3 -1 2 1 1 3 -2 4

  9. (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.

  10. 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)} swap x and y

  11. Find the Inverse • Write the inverse of the following relation as a set of ordered pairs:

  12. First make a table 1. Swap the x and y values 2. Write as a set of ordered pairs: {(3,-1.5),(4,1),(-1,4), (-1,4),(2,5),(-1.5,6)}

  13. Classwork Complete 5-2 Study Guide Worksheet Homework complete section 5-2 (unit outline) Read Section 5-3 Equations as Relations

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