1. Define Inverse Variation #3 Give a real life example

2. The PRODUCT of two variables will always be the same (constant). Example: –The speed, s, you drive and the time, t, it takes for you to get to Rochester. #3

3. State the General Form of an inverse variation equation. Draw an example of a typical inverse variation and name the graph. #4

4. xy = k or. HYPERBOLA (ROTATED) #4

5. FUNCTIONS BLUE CARD

6. Define Domain Define Range #9

7. DOMAIN - List of all possible x- values (aka – List of what x is allowed to be). RANGE – List of all possible y- values. #9

8. Test whether a relation (any random equation) is a FUNCTION or not? #10

9. Vertical Line Test Each member of the DOMAIN is paired with one and only one member of the RANGE. #10

10. Define 1 – to – 1 Function How do you test for one? #11

11. 1-to-1 Function: A function whose inverse is also a function. Horizontal Line Test #11

12. How do you find an INVERSE Function… ALGEBRAICALLY? GRAPHICALLY? #12

13. Algebraically: Switch x and y… …solve for y. Graphically: Reflect over the line y=x #12

14. What notation do we use for Inverse? If point (a,b) lies on f(x)… #13

15. …then point (b,a) lies on Notation: #13

16. f(-x) Identify the action Identify the result #17

17. Action: Negating x Result: Reflection over the y-axis #17

18. -f(x) Identify the action Identify the result #18

19. Action: negating y Result: Reflection over the x-axis #18

20. Exponents

21. When you multiply… the base and the exponents #46

22. KEEP (the base) ADD (the exponents) #46

23. When dividing… the base & the exponents. #47

24. Keep (the base) SUBTRACT (the exponents) #47

25. Power to a power… #48

26. MULTIPLY the exponents #48

27. Negative Exponents… #49

28. Reciprocate the base #49

29. Ground Hog Rule #50

31. Exponential Equations y = a(b) x Identify the meaning of a & b #51

32. Exponential equations occur when the exponent contains a variable a = initial amount b = growth factor b > 1 Growth b < 1 Decay #51

33. Name 2 ways to solve an Exponential Equation #52

34. 1. Get a common base, set the exponents equal 2. Take the log of both sides #52

35. A typical EXPONENTIAL GRAPH looks like… #53

36. Horizontal asymptote y = 0 #53

37. Logarithms

38. Expand 1) Log (ab) 2) Log(a+b) #55

39. 1. log(a) + log (b) 2. Done! #55

40. Expand 1. log (a/b) 2. log (a-b) #56

41. 1. log(a) – log(b) 2. DONE!! #56

42. Expand 1. logx m #57

43. m log x #57

44. Convert exponential to log form 2 3 = 8 #58

46. Convert log form to exponential form log 2 8 = 3 #59

47. Follow the arrows. #59

48. Log Equations 1. every term has a log 2. not all terms have a log #60

49. 1. Apply log properties and knock out all the logs 2. Apply log properties condense log equation convert to exponential and solve #60

50. What does a typical logarithmic graph look like? #61

51. Vertical asymptote at x = 0 #61

52. Change of Base Formula What is it used for? #62

53. Used to graph logs #62

54. EXACT TRIG VALUES

55. sin 30 or sin #66

57. sin 60 or sin #67

59. sin 45 or sin #68

61. sin 0 #69

62. 0

63. sin 90 or sin #70

64. 1

65. sin 180 or sin #71

66. 0

67. sin 270 or sin #72

68. #72

69. sin 360 or sin #73

70. 0

71. cos 30 or cos #74

73. cos 60 or cos #75

75. cos 45 or cos #76

77. cos 0 #77

78. 1

79. cos 90 or cos #78

80. 0

81. cos 180 or cos #79

82. #79

83. cos 270 or cos #80

84. 0

85. cos 360 or cos #81

86. 1

87. tan 30 or tan #82

89. tan 60 or tan #83

91. tan 45 or tan #84

92. 1

93. tan 0 #85

94. 0

95. tan 90 or tan #86

96. D.N.E. or Undefined #86

97. tan 180 or tan #87

98. 0

99. tan 270 or tan #88

100. D.N.E. Or Undefined #88

101. tan 360 or tan #89

102. 0

103. Trigonometry Identities

104. Reciprocal Identity sec = #90

106. Reciprocal Identity csc = #91

108. cot = Reciprocal Identity #92

110. Quotient Identity #93

112. Trig Graphs

113. Amplitude #94

114. Height from the midline y = asin(fx) y = -2sinx amp = 2 #94

115. Frequency #95

116. How many complete cycles between 0 and #95

117. Period #96

118. How long it takes to complete one full cycle Formula: #96

119. y = sinx a) graph b) amplitude c) frequency d) period e) domain f) range #97

120. a) b) 1 c) 1 d) e) all real numbers f) #97

121. y = cosx a) graph b) amplitude c) frequency d) period e) domain f) range #98

122. a) b) 1 c) 1 d) e) all real numbers f) #98

123. y = tan x a) graph b) amplitude c) asymptotes at… #99

124. a) b) No amplitude c) Asymptotes are at odd multiplies of Graph is always increasing #99

125. y = csc x A) graph B) location of the asymptotes #100

126. b) Asymptotes are multiples of Draw in ghost sketch #100

127. y = secx A) graph B) location of the asymptotes #101

128. B) asymptotes are odd multiples of Draw in ghost sketch #101

129. y=cotx A) graph B) location of asymptotes #102

130. B) multiplies of Always decreasing #102