Section 2.5 Transformation of Functions

1. Section 2.5Transformation of Functions

2. Graphs of Common Functions

6. Reciprocal Function

7. Vertical Shifts

9. Vertical Shifts

11. Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2

12. Horizontal Shifts

14. Horizontal Shifts

15. Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2

16. Combining Horizontal and Vertical Shifts

17. Example Use the graph of f(x)=x2 to obtain g(x)=(x+1)2+2

18. Reflections of Graphs

20. Reflections about the x-axis

22. Example Use the graph of f(x)=x3 to obtain the graph of g(x)= (-x)3.

23. Example

24. Vertical Stretching and Shrinking

26. Vertically Shrinking

27. Vertically Stretching Graph of f(x)=x3 Graph of g(x)=3x3 This is vertical stretching – each y coordinate is multiplied by 3 to stretch the graph.

28. Example Use the graph of f(x)=|x| to graph g(x)= 2|x|

29. Horizontal Stretching and Shrinking

31. Horizontal Shrinking

32. Horizontal Stretching

33. Example

34. Sequences of Transformations

35. A function involving more than one transformation can be graphed by performing transformations in the following order: • Horizontal shifting • Stretching or shrinking • Reflecting • Vertical shifting

36. Summary of Transformations

37. A Sequence of Transformations Starting graph. Move the graph to the left 3 units Stretch the graph vertically by 2. Shift down 1 unit.

38. Example

39. Example

40. Example

41. (a) (b) (c) (d)

42. g(x) Write the equation of the given graph g(x). The original function was f(x) =x2 (a) (b) (c) (d)

43. g(x) Write the equation of the given graph g(x). The original function was f(x) =|x| (a) (b) (c) (d)