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5-2 Relations

This lesson explores the concepts of domain, range, and inverse of a function, demonstrating how to represent relations through various formats, including ordered pairs, tables, mappings, and graphs. Students will graph specific points, identify their quadrants, and engage in guided practice with examples. The session includes exercises to swap coordinates for inverse relations and utilize mappings for visual representation. The material integrates biology concepts through the classification of microorganisms, adding a cross-disciplinary perspective to the understanding of mathematical relations.

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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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