Section 2.5 Transformation of Functions
Graphs of Common Functions
 
 
 
Reciprocal Function
Vertical Shifts
 
Vertical Shifts
 
Example Use the graph of f(x)=|x| to obtain g(x)=|x|-2
Horizontal Shifts
 
Horizontal Shifts
Example Use the graph of f(x)=x 2  to obtain g(x)=(x+1) 2
Combining Horizontal and Vertical Shifts
Example Use the graph of f(x)=x 2  to obtain g(x)=(x+1) 2 +2
Reflections of Graphs
 
Reflections about the x-axis
 
Example Use the graph of f(x)=x 3  to obtain the graph of g(x)= (-x) 3 .
Example
Vertical Stretching and Shrinking
 
Vertically Shrinking
Vertically Stretching Graph of f(x)=x 3 Graph of g(x)=3x 3 This is vertical stretching – each y coordinate is multiplied b...
Example Use the graph of f(x)=|x|  to graph g(x)= 2|x|
Horizontal Stretching and Shrinking
 
Horizontal Shrinking
Horizontal Stretching
Example
Sequences of Transformations
<ul><li>A function involving more than one transformation can be graphed by performing transformations in the following or...
Summary of Transformations
A Sequence of Transformations Move the graph to the left 3 units Starting graph . Stretch the graph vertically by 2. Shift...
Example
Example
Example
(a)  (b) (c) (d)
(a)  (b) (c) (d) Write the equation of the given graph g(x).  The original function was  f(x) =x 2 g(x)
(a)  (b) (c) (d) Write the equation of the given graph g(x).  The original function was  f(x) =|x| g(x)
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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)

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