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Relations: Representations and Interpretations

Learn how to represent relations using tables, graphs, and mappings and interpret graphs of relations. Practice determining the domain and range of relations.

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Relations: Representations and Interpretations

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  1. Splash Screen

  2. Warm-Up Graph these points: (5,4), (-3,2) and (0, -4)

  3. 1.6 Relations OBJECTIVES • Represent relations. • Interpret graphs of relations.

  4. A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. Representations of a Relation Table List the x-coordinates in the first column and the corresponding y-coordinates in the second column. Example 1

  5. A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. Graph Graph each ordered pair on a coordinate plane. Example 1

  6. Domain Range A. Express the relation {(4, 3), (–2, –1), (2, –4), (0, –4)} as a table, a graph, and a mapping. MappingList the x-values in the domain and the y-values in the range. Draw an arrow from the x-value to the corresponding y-value. Example 1

  7. B. Determine the domain and range for the relation {(4, 3), (–2, –1), (2, –4), (0, –4)}. Representations of a Relation Answer: The domain for this relation is {4, –2, 2, 0}. The range is {3, –1, –4}. Example 1

  8. 1.) Write the relation as a table, graph, and mapping . {(4,-5), (6,2), (3,4), (-1,-5), (8,1)} 2.) State the domain and range of the relation. PRACTICE Practice

  9. B. Determine the domain and range of the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}. • D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6} • D = {–2, 2, 3, 6}; R = {–1, 3, 4, 5} • D = {–1, 3}; R = {–2, 2} • D = {4}; R = {4} Example 1

  10. VOCABULARY: • Independent Variable: a variable that is not affected by another variable. • Dependent Variable: a variable that is affected or relies on another variable. Independent Vs. Dependent

  11. Independent and Dependent Variables A. CLIMATEIn warm climates, the average amount of electricity used rises as the daily average temperature increases, and falls as the daily average temperature decreases. Identify the independent and the dependent variables for this function. Answer: Temperature is the independent variable, as it is unaffected by the amount of electricity used. Electricity usage is the dependent variable, as it is affected by the temperature. Example 2

  12. Independent and Dependent Variables B. The number of calories you burn increases as the number of minutes that you walk increases. Identify the independent and the dependent variables for this function. Answer: The time is the independent variable. The number of calories burned is the dependent variable, as it is affected by the time. Example 2

  13. Analyze Graphs The graph represents the temperature in Ms. Ling’s classroom on a winter school day. Describe what is happening in the graph. Sample answer: The temperature increases after the heat is turned on. Then the temperature fluctuates up and down because of the thermostat. Finally, the temperature drops when the heat is turned off. Example 3

  14. The graph represents Macy’s speed as she swims laps in a pool. Describe what is happening in the graph. A. Macy is doing bobs. B. Macy’s speed increases as she crosses the length of the pool, but then decreases to zero when she turns around at the end of each lap. C. Macy is swimming at a constant speed. D. Macy’s speed continues to decrease. Example 3

  15. Exit Slip: Each write a sentence or two summarizing what you learned today. HOMEWORK: P. 43-45 #14-18, 27, 28, 30 End of the Lesson

  16. A. In a particular club, as membership dues increase, the number of new members decreases. Identify the independent and dependent variable in this function. A. The number of new members is the independent variable. The dues is the dependent variable. B. Membership dues is the independent variable. The number of new members is the dependent variable. C.x is the independent variable. y is the dependent variable. D. Both variables are independent. Example 2

  17. A.C. B.D. A. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)} as a mapping. Example 1

  18. Using the following ordered pairs; represent the relation in at least two other ways. {(1,3), (1,5), (5,3), (2,1)}

  19. B. The area of a square increases as the length of a side increases. Identify the independent and dependent variable in this function. A. The length of the side is independent, and the the area of the square is dependent. B. The area is independent, and the side length is dependent. C. Both variables are independent. D. Both variables are dependent. Example 2

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