1. 7.1 N th Roots and Rational Exponents 7.2 Properties of Rational Exponents 7.3 Power Functions and Function Operations 7.4 Inverse Functions 7.5 Graphing Square Root and Cube Root Functions 7.6 Solving Radical Equations Homework Assignments OPENERS EXTRA REVIEW: Domain and Range EXTRA REVIEW: No Calculator EXTRA REVIEW: Ugly Radicals CH 7 Powers Roots Radicals,

2. 7.1 Roots and Rational Exponents EXPONENT RULE #1

3. CH 7 Powers Roots Radicals 7.1 Roots and Rational Exponents

4. CH 7 Powers Roots Radicals 7.1 Roots and Rational Exponents

5. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

6. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

7. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

8. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

9. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

10. Practice problems: Simplify each of the following. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

11. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

12. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

13. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

14. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

15. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

16. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

17. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

18. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents I’m Confused!!! I don’t get this stuff and we have a quiz on it tomorrow!

19. CH 7 Powers Roots Radicals 7.2 Properties of Rational Exponents

20. CH 7 Powers Roots Radicals 7.3 Power Functions

21. CH 7 Powers Roots Radicals 7.3 Power Functions

22. We can write this as: f(3)+g(3) or f + g (3) or (f + g) (3) CH 7 Powers Roots Radicals 7.3 Power Functions

23. This means we are going to take the equations (with x still in them) and add them together. CH 7 Powers Roots Radicals 7.3 Power Functions

24. CH 7 Powers Roots Radicals 7.3 Power Functions

25. This means we are going to find g(27) Then put that answer into f(x) CH 7 Powers Roots Radicals 7.3 Power Functions

26. CH 7 Powers Roots Radicals 7.3 Power Functions

27. OK, this is the hard part. We are going to put an entire equation into the other equation, without putting in a number for x CH 7 Powers Roots Radicals 7.3 Power Functions

28. CH 7 Powers Roots Radicals 7.3 Power Functions

29. CH 7 Powers Roots Radicals 7.3 Power Functions

30. Click for Composite Function Activity Click for Extra Function Practice

31. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN and RANGE: The DOMAIN and RANGE are properties of an equation. They Tell you… …what numbers can go IN to an equation. and …what numbers can come OUT of an equation

32. DOMAIN RANGE INPUT The numbers we put into the equation are called the The numbers we get out of the equation are called the OUTPUT CH 7 Powers Roots Radicals 7.3 Power Functions

33. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. RANGE: The list of all possible outputs for a function.

34. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. For many functions, there is no restriction for what we can put into it. If there is no restriction, we say the domain is “ALL REAL NUMBERS” You can put any number you can think of in for x.

35. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. There are some functions that do have restrictions. For each of the following problems, there are numbers that we are NOT allowed to use for x. Domain:

36. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: The list of all possible inputs for a function. Domain:

37. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

38. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

39. CH 7 Powers Roots Radicals 7.3 Power Functions DOMAIN: You can use the graph to help identify the domain Domain:

40. CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

41. CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

42. CH 7 Powers Roots Radicals 7.3 Power Functions RANGE: The list of all possible outputs for a function. RANGE:

43. CH 7 Powers Roots Radicals 7.4 Inverse Functions

44. CH 7 Powers Roots Radicals 7.4 Inverse Functions

45. If Then To prove that two functions are inverses… Show that the composite functions cancel out AND CH 7 Powers Roots Radicals 7.4 Inverse Functions

46. FIND THE INVERSE OF A POWER FUNCTION CH 7 Powers Roots Radicals 7.4 Inverse Functions

47. IMPORTANT SIDE_NOTE CH 7 Powers Roots Radicals 7.4 Inverse Functions

48. CH 7 Powers Roots Radicals 7.4 Inverse Functions

49. -2 0 1 2 3 -4 2 5 8 11 -4 2 5 8 11 -2 0 1 2 3 CH 7 Powers Roots Radicals 7.4 Inverse Functions

50. 0,7 -8,0 7,0 0,-8 CH 7 Powers Roots Radicals 7.4 Inverse Functions

51. CH 7 Powers Roots Radicals 7.4 Inverse Functions

52. CH 7 Powers Roots Radicals 7.4 Inverse Functions

53. INVERSES CH 7 Powers Roots Radicals 7.3 Power Functions

54. INVERSES CH 7 Powers Roots Radicals 7.3 Power Functions

55. NOW FIND THE INVERSE FUNCTION Its like going backwards Switch x and y Resolve for y CH 7 Powers Roots Radicals 7.3 Power Functions

56. DO YOU KNOW………. How to find the inverse of a function? Verify that 2 functions are inverses? How to identify inverses from their graphs? Tell if an equation and it’s inverse are functions?

57. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

58. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

59. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

60. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

61. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

62. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

63. X Min: -10 X Max: 10 Y Min: -200 Y Max: 200 CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

64. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

65. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

66. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

67. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

68. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

69. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

70. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

71. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

72. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

73. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

74. CH 7 Powers Roots Radicals 7.5 Square and Cube Root Graphs

75. CH 7 Powers Roots Radicals 7.6 Solve Radical Equations

76. CH 7 Powers Roots Radicals Homework Homework Assignments: Worksheet 7.1 p. 411 Pamphlet 7.1-7.4 p. 418 p. 426 p. 441

77. A A B C D E F G H I J K L M N OBCDEFGHI JKLMNO CH 7 Powers Roots Radicals OPENERS

78. 1 CH 7 Powers Roots Radicals OPENERS A

79. 1 CH 7 Powers Roots Radicals OPENERS B

80. The population of Utah grows at a rate of Where y is the population, and x is the year. In what year was the population 308,268? CH 7 Powers Roots Radicals OPENERS C

81. 1 CH 7 Powers Roots Radicals OPENERS D

82. 1 CH 7 Powers Roots Radicals OPENERS E

83. 1 CH 7 Powers Roots Radicals OPENERS F

84. 1 CH 7 Powers Roots Radicals OPENERS G

85. 1 CH 7 Powers Roots Radicals OPENERS H

86. 1 CH 7 Powers Roots Radicals OPENERS I

87. 1 CH 7 Powers Roots Radicals OPENERS J

88. 1 CH 7 Powers Roots Radicals OPENERS K

89. CH 7 Powers Roots Radicals OPENERS L

90. CH 7 Powers Roots Radicals OPENERS M

91. CH 7 Powers Roots Radicals OPENERS N

92. State the domain for each of the following: 1.2. 3.4. 5.6. 7.8. 9.10. CH 7 Powers Roots Radicals Extra Review Domain and Range R R R R R R R R R R How does Domain always start ? Which problems have the fraction restriction? Which problems have the even root restriction?

93. State the range for each of the following: 1.2. 3.4. 5.6. 7.8. CH 7 Powers Roots Radicals Extra Review Domain and Range How do we start? For range, we only discussed the restriction when taking even roots. R R RR R R R R

94. State the range for each of the following: 1.2. 3.4. 5.6. 7.8. 9.10. CH 7 Powers Roots Radicals Extra Review: No Calc

95. State the range for each of the following: 1.2. CH 7 Powers Roots Radicals Extra Review: Ugly Radicals

96. State the range for each of the following: 3. CH 7 Powers Roots Radicals Extra Review: Ugly Radicals