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08/01/2013 Linear Relations and Functions Chapter 2 .7 Pg 109

08/01/2013 Linear Relations and Functions Chapter 2 .7 Pg 109. Parent Functions and Transformations. Terminology : Family of graphs, parent graph, parent function, constant function, identity function, quadratic function, translation, reflection, line of reflection , dilation.

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08/01/2013 Linear Relations and Functions Chapter 2 .7 Pg 109

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  1. 08/01/2013Linear Relations and FunctionsChapter 2 .7 Pg 109 Parent Functions and Transformations

  2. Terminology : • Family of graphs, • parent graph, • parent function, • constant function, • identity function, quadratic function, translation, reflection, • line of reflection , • dilation Terminology/Keywords

  3. Parent Functions

  4. 1.Identify a function given the graph. 2. Describe and graph translations. 3. Describe and graph Reflections. 4.Identify Transformations. 5.Real Life Problems. Learning Objectives

  5. Warm Up!Draw the following graphs

  6. Classwork Pages 113 – 116 Exercises 1-8,9,10 – 13 • 33 to 38 • Bonus: 44 ,49 to 51 • Homework Page 116 • Exercises: 50.51 • Practice Worksheet • See website and Email PRACTICE

  7. Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families offunctions. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.

  8. The following basic graphs will be used extensively in this section. It is important to be able to sketch these from memory.

  9. The identity functionf(x) = x

  10. The quadratic function

  11. We will now see how certain transformations (operations) of a function change its graph. This will give us a better idea of how to quickly sketch the graph of certain functions. The transformations are (1) translations, (2) reflections, and (3) stretching/dilation

  12. Parent Functions

  13. a = adjusting shape (compress, stretch or reflect) c = moving up/down d = moving left/right Note: a ,c ,d  R Remember f(x) means – function with variable x Recall “Transforming”

  14. f(x) = x2 f(x) + y y 0 = x2 0 1 = x2 +1 3 = x2 + 3 2 = x2+2 x Vertical Translations

  15. f(x) = x2 f(x) + y y 0 = x2 -1 = x2 -1 0 -3 = x2-3 -2 =x2 - 2 x Vertical Translations Adding c to f(x) moves the graph up by c units if c is positive, down if c is negative

  16. f(x) = x2 y y f(x + 0) = (x+0)2 f(x+1)=(x+1)2 f(x+2) =(x+2)2 f(x+3) = (x+3)2 x Horizontal Translations

  17. f(x) = x2 y y f(x – 0) = (x-0)2 f(x-1)=(x-1)2 f(x-2) =(x-2)2 f(x-3) = (x-3)2 x • Changing a function from f(x) to f(x-d) will move the graph d units to the right. • Changing a function from f(x) to f(x+d) will move the graph d units to the left. Horizontal Translations

  18. If f(x) = x2, graph f(x-2) +3: y y f(x) = x2 f(x-2)=(x-2)2 f(x-2) +3 =(x-2)2 +3 x Combining Translations

  19. Lesson Quiz: Part I Identify the parent function for g from its function rule. Then graph gby using grapher on your laptop and describe what transformation of the function it represents. 1.g(x) = x + 7 linear; translation up 7 units

  20. Lesson Quiz: Part II Identify the parent function for g from its function rule. Then graph g and describe what transformation of the parent function it represents. 2.g(x) = x2 – 7 quadratic; translation down 7 units

  21. Check It Out! The cost of playing an online video game depends on the number of months for which the online service is used. Graph the relationship from number of months to cost, and identify which parent function best describes the data. Then use the graph to estimate the cost of 5 months of online service.

  22. Check It Out! Example 3 Continued Step 1 Graph the relation. Graph the points given in the table. Draw a smooth line through them to help you see the shape. Step 2 Identify the parent function. The graph of the data set resembles the shape of a linear parent function ƒ(x) = x. Step 3 Estimate the cost for 5 months of online service. The linear graph indicates that the cost for 5 months of online service is $72.

  23. Lesson Quiz: Part I Identify the parent function for g from its function rule. Then graph g on your laptop and describe what transformation of the parent function it represents. 1.g(x) = x + 7 linear; translation up 7 units

  24. Lesson Quiz: Part II Identify the parent function for g from its function rule. Then graph g on your laptop and describe what transformation of the parent function it represents. 2.g(x) = x2 – 7 quadratic; translation down 6 units

  25. Lesson Quiz: Part III 3. Stacy earns $7.50 per hour. Graph the relationship from hours to amount earned and identify which parent function best describes it. Then use the graph to estimate how many hours it would take Stacy to earn $60. linear: 8 hr

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