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### 2 5 Bzca5e

1. 1. Section 2.5 Transformation of Functions
2. 2. Graphs of Common Functions
3. 6. Reciprocal Function
4. 7. Vertical Shifts
5. 9. Vertical Shifts
6. 11. Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2
7. 12. Horizontal Shifts
8. 14. Horizontal Shifts
9. 15. Example Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2
10. 16. Combining Horizontal and Vertical Shifts
11. 17. Example Use the graph of f(x)=x 2 to obtain g(x)=(x+1) 2 +2
12. 18. Reflections of Graphs
13. 20. Reflections about the x-axis
14. 22. Example Use the graph of f(x)=x 3 to obtain the graph of g(x)= (-x) 3 .
15. 23. Example
16. 24. Vertical Stretching and Shrinking
17. 26. Vertically Shrinking
18. 27. Vertically Stretching Graph of f(x)=x 3 Graph of g(x)=3x 3 This is vertical stretching – each y coordinate is multiplied by 3 to stretch the graph.
19. 28. Example Use the graph of f(x)=|x| to graph g(x)= 2|x|
20. 29. Horizontal Stretching and Shrinking
21. 31. Horizontal Shrinking
22. 32. Horizontal Stretching
23. 33. Example
24. 34. Sequences of Transformations
25. 35. <ul><li>A function involving more than one transformation can be graphed by performing transformations in the following order: </li></ul><ul><li>Horizontal shifting </li></ul><ul><li>Stretching or shrinking </li></ul><ul><li>Reflecting </li></ul><ul><li>Vertical shifting </li></ul>
26. 36. Summary of Transformations
27. 37. A Sequence of Transformations Move the graph to the left 3 units Starting graph . Stretch the graph vertically by 2. Shift down 1 unit.
28. 38. Example
29. 39. Example
30. 40. Example
31. 41. (a) (b) (c) (d)
32. 42. (a) (b) (c) (d) Write the equation of the given graph g(x). The original function was f(x) =x 2 g(x)
33. 43. (a) (b) (c) (d) Write the equation of the given graph g(x). The original function was f(x) =|x| g(x)