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Splash Screen. Five-Minute Check (over Lesson 2–6) CCSS Then/Now New Vocabulary Key Concept: Parent Functions Example 1: Identify a Function Given the Graph Example 2: Describe and Graph Translations Example 3: Describe and Graph Reflections Example 4: Describe and Graph Dilations

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 2–6) CCSS Then/Now New Vocabulary Key Concept: Parent Functions Example 1: Identify a Function Given the Graph Example 2: Describe and Graph Translations Example 3: Describe and Graph Reflections Example 4: Describe and Graph Dilations Example 5: Real-World Example: Identify Transformations Concept Summary: Transformations of Functions Lesson Menu

  3. Identify the type of function represented by the graph. A. linear B. piecewise-defined C. absolute value D. parabolic 5-Minute Check 1

  4. Identify the type of function represented by the graph. A. linear B. piecewise-defined C. absolute value D. parabolic 5-Minute Check 1

  5. Identify the type of function represented by the graph. A. piecewise-defined B. linear C. parabolic D. absolute value 5-Minute Check 2

  6. Identify the type of function represented by the graph. A. piecewise-defined B. linear C. parabolic D. absolute value 5-Minute Check 2

  7. A. $60 B. $101 C. $102 D. $148 5-Minute Check 3

  8. A. $60 B. $101 C. $102 D. $148 5-Minute Check 3

  9. Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Mathematical Practices 6 Attend to precision. CCSS

  10. You analyzed and used relations and functions. • Identify and use parent functions. • Describe transformations of functions. Then/Now

  11. family of graphs • reflection • line of reflection • dilation • parent graph • parent function • constant function • identity function • quadratic function • translation Vocabulary

  12. Concept

  13. Identify a Function Given the Graph A.Identify the type of function represented by the graph. Answer: Example 1

  14. Identify a Function Given the Graph A.Identify the type of function represented by the graph. Answer: The graph is a V shape. So, it is an absolute value function. Example 1

  15. Identify a Function Given the Graph B. Identify the type of function represented by the graph. Answer: Example 1

  16. Identify a Function Given the Graph B. Identify the type of function represented by the graph. Answer: The graph is a parabola, so it is a quadratic function. Example 1

  17. A. Identify the type of function represented be the graph. A. absolute value function B. constant function C. quadratic function D. identity function Example 1

  18. A. Identify the type of function represented be the graph. A. absolute value function B. constant function C. quadratic function D. identity function Example 1

  19. B. Identify the type of function represented be the graph. A. absolute value function B. constant function C. quadratic function D. identity function Example 1

  20. B. Identify the type of function represented be the graph. A. absolute value function B. constant function C. quadratic function D. identity function Example 1

  21. Describe and Graph Translations Describe the translation in y = (x + 1)2. Then graph the function. Answer: Example 2

  22. Describe and Graph Translations Describe the translation in y = (x + 1)2. Then graph the function. Answer: The graph of the function y = (x + 1)2 is a translation of the graph of y = x2 left 1 unit. Example 2

  23. Describe the translation in y = |x – 4|. Then graph the function. A. translation of the graph y = |x| up 4 units B. translation of the graph y = |x| down 4 units C. translation of the graph y = |x| right 4 units D. translation of the graph y = |x| left 4 units Example 2

  24. Describe the translation in y = |x – 4|. Then graph the function. A. translation of the graph y = |x| up 4 units B. translation of the graph y = |x| down 4 units C. translation of the graph y = |x| right 4 units D. translation of the graph y = |x| left 4 units Example 2

  25. Describe and Graph Reflections Describe the reflection in y = –|x|. Then graph the function. Answer: Example 3

  26. Describe and Graph Reflections Describe the reflection in y = –|x|. Then graph the function. Answer: The graph of the function y = –|x| is a reflection of the graph of y = |x| across the x-axis. Example 3

  27. Describe the reflection in y = –x2. Then graph the function. A. reflection of the graph y = x2 across the x-axis B. reflection of the graph y = x2 across the y-axis C. reflection of the graph y = x2 across the line x = 1. D. reflection of the graph y = x2 across the x = –1 Example 3

  28. Describe the reflection in y = –x2. Then graph the function. A. reflection of the graph y = x2 across the x-axis B. reflection of the graph y = x2 across the y-axis C. reflection of the graph y = x2 across the line x = 1. D. reflection of the graph y = x2 across the x = –1 Example 3

  29. Describe the dilation on Then graph the function. Describe and Graph Dilations Answer: Example 4

  30. Describe the dilation on Then graph the function. Answer: The graph of is a dilation that compresses the graph of vertically. Describe and Graph Dilations Example 4

  31. Describe the dilation in y = |2x|. Then graph the function. A. dilation of the graph of y = |x| compressed vertically B. dilation of the graph of y = |x| stretched vertically C. dilation of the graph of y = |x| translated 2 units up D. dilation of the graph of y = |x| translated 2 units right Example 4

  32. Describe the dilation in y = |2x|. Then graph the function. A. dilation of the graph of y = |x| compressed vertically B. dilation of the graph of y = |x| stretched vertically C. dilation of the graph of y = |x| translated 2 units up D. dilation of the graph of y = |x| translated 2 units right Example 4

  33. Identify Transformations Example 5

  34. Identify Transformations Example 5

  35. Identify Transformations Example 5

  36. Which of the following is not an accurate description of the transformations in the function ? A.+4 translates f(x) = |x| right 4 units B.–2 translates f(x) = |x| down 2 units C. reflects f(x) = |x| across the x-axis D. +4 translates f(x) = |x| left 4 units Example 5

  37. Which of the following is not an accurate description of the transformations in the function ? A.+4 translates f(x) = |x| right 4 units B.–2 translates f(x) = |x| down 2 units C. reflects f(x) = |x| across the x-axis D. +4 translates f(x) = |x| left 4 units Example 5

  38. Concept

  39. End of the Lesson

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