1. Functions
Domain and Range

2. DOMAIN

3. WHAT CAN YOU SUBSTITUTE IN FOR x
WHAT CAN x BE or
WHAT CAN YOU SUBSTITUTE IN FOR x

4. When NO Domain is specified we are to assume in MOST cases that

5. Function
DOMAIN
Interval Notation
Interval Notation
Interval Notation

6. There are Exceptions

7. FRACTIONS

8. First Example

9. x’s in the denominator
WHAT CAN’T x BE

10. DOMAIN
WHAT CAN’T x BE

11. DOMAIN or
Interval Notation

12. Next Example

13. x’s in the numerator
DOMAIN or
Interval Notation

14. Next Example

15. x’s in the denominator
WHAT CAN’T x BE

16. x’s in the denominator
WHAT CAN’T x BE
DOMAIN

17. x’s in the denominator
WHAT CAN’T x BE
DOMAIN

18. DOMAIN or
Interval Notation

19. Next Example

20. x’s in the denominator
WHAT CAN’T x BE
Always True!

21. x’s in the denominator
WHAT CAN’T x BE
DOMAIN

22. x’s in the denominator
WHAT CAN’T x BE
DOMAIN or
Interval Notation

23. Next Example

24. x’s in the denominator
WHAT CAN’T x BE

25. x’s in the denominator
WHAT CAN’T x BE
DOMAIN

26. x’s in the denominator
WHAT CAN’T x BE
DOMAIN

27. DOMAIN or
Interval Notation

28. Next Example

29. WHAT CAN’T x BE

30. WHAT CAN’T x BE
DOMAIN

31. DOMAIN or
Interval Notation

32. WHAT CAN’T x BE
What Else?

33. ROOTS

34. First Example

35. x’s under the
Square root
WHAT CAN’T x BE ?

36. Can x be a positive number?
Example
What number times itself is equal to 4? OK

37. What number times itself is equal to 0?
Can x be zero? ?
Example
What number times itself is equal to 0? OK

38. Can x be a negative number?
Example
What number times itself is equal to - 4?
NO WAY

39. How do we write that mathematically?
x can be a positive number
x can be zero
x cannot be a negative number
How do we write that mathematically?

40. GO BACK

41. x’s under the
Square root
DOMAIN

42. x’s under the
Square root
DOMAIN

43. DOMAIN or
Interval Notation

44. Next Example

45. x’s under the Square root WHAT CAN’T x BE
Whatever is under the square root sign has to be greater than or equal to zero!
It can’t be negative

46. x’s under the
Square root
WHAT CAN’T x BE
You Solve

47. x’s under the
Square root
WHAT CAN’T x BE

48. x’s under the
Square root
WHAT CAN’T x BE
DOMAIN

49. x’s under the
Square root
WHAT CAN’T x BE
DOMAIN

50. DOMAIN or
Interval Notation

51. x’s under the WHAT CAN’T x BE
Square root
WHAT CAN’T x BE
Whatever is under the square root sign has to be greater than or equal to zero!
It can’t be negative

52. x’s under the
Square root
WHAT CAN’T x BE
You Solve

53. x’s under the
Square root
WHAT CAN’T x BE

54. x’s under the
Square root
WHAT CAN’T x BE
Always True!

55. x’s under the
Square root
WHAT CAN’T x BE
DOMAIN or
Interval Notation

56. Next Example

57. x’s under the
Square root
WHAT CAN’T x BE

58. x’s under the
Square root
WHAT CAN’T x BE

59. x’s under the
Square root
WHAT CAN’T x BE
DOMAIN

60. x’s under the
Square root
WHAT CAN’T x BE
DOMAIN

61. DOMAIN or
Interval Notation

62. RANGE

63. Function Machine

64. Function Machine

65. Function Machine

66. Function Machine

67. Function Machine

68. Function Machine

69. Function Machine

70. Function Machine

71. Function Machine

72. Function Machine

73. What Real Number could this function never produced
Function Machine
What Real Number could this function never produced

74. Function Machine

75. Function Machine

76. Interval Notation or

77. STAT PLOT OFF
Clear y = then enter
Zoom 6:ZStandard

79. What About
Never touches

80. What About

81. What About

82. Use your Graphing Calculator to find the Range
You Try
Use your Graphing Calculator to find the Range

83. Answers

84. Answers