1. or
ODD
EVEN
Functions

2. TESTING FUNCTION FOR
SYMMETRY

3. Test a function for symmetry with respect to the y-axis
Substitute –x for x and see if you have equivalent functions

4. Symmetry
equivalent to

5. SYMMETRIC WITH RESPECT TO the y-axis
EVEN FUNCTION

6. NEXT

7. Test for symmetry of a function with respect to the origin
Substitute –x for x and –f(x) for f(x) and see if you have equivalent functions

10. Symmetry
equivalent to

11. SYMMETRIC WITH RESPECT TO THE ORIGIN
ODD FUNCTION

12. Why don’t we talk about FUNCTIONS symmetric with respect to:
x-axis
NOT A
FUNCTION

13. First Example

14. Determine whether each function is even, odd, or neither

15. Determine whether each function is even, odd, or neither
Simplify

16. Determine whether each function is even, odd, or neither
Simplify

17. Determine whether each function is even, odd, or neither
Simplify

18. Determine whether each function is even, odd, or neither
Simplify

19. Determine whether each function is even, odd, or neither
COMPARE ?
EVEN
YES

20. NEXT EXAMPLE

21. Determine whether each function is even, odd, or neither

22. Determine whether each function is even, odd, or neither
Simplify

23. Determine whether each function is even, odd, or neither
Simplify

24. Determine whether each function is even, odd, or neither
Simplify

25. Determine whether each function is even, odd, or neither
COMPARE ? NO

26. Determine whether each function is even, odd, or neither
COMPARE
NOT
EVEN ?

27. Now See If It's
ODD

28. Determine whether each function is even, odd, or neither
Start Here
Need

29. Determine whether each function is even, odd, or neither

30. Determine whether each function is even, odd, or neither

31. Determine whether each function is even, odd, or neither

32. Determine whether each function is even, odd, or neither

33. Determine whether each function is even, odd, or neither
COMPARE ?
YES
ODD

34. NEXT EXAMPLE

35. Determine whether each function is even, odd, or neither

36. Determine whether each function is even, odd, or neither

37. Determine whether each function is even, odd, or neither

38. Determine whether each function is even, odd, or neither

39. Determine whether each function is even, odd, or neither

40. Determine whether each function is even, odd, or neither
COMPARE ? NO

41. Determine whether each function is even, odd, or neither
COMPARE
NOT
EVEN ?

42. Now See If It's
ODD

43. Determine whether each function is even, odd, or neither
Start Here
Need

44. Determine whether each function is even, odd, or neither

45. Determine whether each function is even, odd, or neither

46. Determine whether each function is even, odd, or neither

47. Determine whether each function is even, odd, or neither

48. Determine whether each function is even, odd, or neither

49. Determine whether each function is even, odd, or neither
COMPARE ? NO

50. Determine whether each function is even, odd, or neither
COMPARE
NOT
ODD ?

51. Determine whether each function is even, odd, or neither
COMPARE
NOT
EVEN
NOT
ODD ?

52. Determine whether each function is even, odd, or neither
COMPARE ?
Neither

53. SYMMETRIC WITH RESPECT TO the y-axis
EVEN FUNCTION

54. SYMMETRIC WITH RESPECT TO THE ORIGIN
ODD FUNCTION

55. NOT EVEN
NOT ODD
Neither

56. Graphic
Examples

57. Even, Odd, Neither? ?

58. SYMMETRIC WITH RESPECT TO the y-axis
Even, Odd, Neither?
SYMMETRIC WITH RESPECT TO the y-axis

59. Even, Odd, Neither?
EVEN

60. NEXT

61. Even, Odd, Neither? ?

62. SYMMETRIC WITH RESPECT TO THE ORIGIN

63. SYMMETRIC WITH RESPECT TO THE ORIGIN

64. Even, Odd, Neither?
ODD

65. NEXT

66. Even, Odd, Neither? ?

67. Even, Odd, Neither?
Neither