1. 1.4 Absolute Values Solving Absolute Value Equations By putting into one of 3 categories

2. What is the definition of “Absolute Value”? __________________________________ Mathematically, ___________________ For example, in, where could x be? 0 -3 3

3. To solve these situations, __________________________________ __________________________________ __________________________________ Consider ________________________ 0

4. That was Category 1 Category 1 : ____________________________ _______________________________________ ExampleCase 1Case 2

5. Absolute Value Inequalities Think logically about another situation. What does mean? For instance, in the equation, _________________________________ 0

6. How does that translate into a sentence? __________________________________ Now solve for x. This is Category 2: when x is less than a number

7. Absolute Value Inequalities What does mean? In the equation, __________________________________ 0

8. Less than = And statement Greater than = Or statement Note:  is the same as  ;  is the same as  ; just have the sign in the rewritten equation match the original.

9. Isolate Absolute Value _______________________________________ ______________________________________

10. When x is on both sides ______________________________________ ________________________________________ ______________________________________ Case 1Case 2

11. Example inequality with x on other side Case 1Case 2

12. Examples Case 1 Case 2

15. _________________________________ Whats wrong with this?__________________________________________

17. 1-4 Compound Absolute Values Equalities and Inequalities More than one absolute value in the equation

18. Some Vocab Domain- _________________________ Range- __________________________ Restriction- _______________________ ______________________________________ ____________________________

19. Find a number that works. We will find a more methodical approach to find all the solutions.

20. In your approach, think about the values of this particular mathematical statement in the 3 different areas on a number line. -_________________________________________ -________________________________________

21. It now forms 3 different areas or cases on the number line. ______________________________ ___________________________________

22. Case 1 Domain ________________________ ____________________________________________________ _________________________________ _________________________________ _________________________________

23. Case 2 Domain ___________________________________

24. Case 3 Domain _____________________________

25. Final Answers ______________________________ _____________________________ 5 2 -2

26. If you get an answer in any of the cases where the variable disappears and the answer is TRUE ________________________________ ________________________________ ________________________________ ________________________________

28. 1-5 Exponential Rules You know these already

29. Review of the Basics

30. Practice problems Simplify each expression

32. Do NOT use calculators on the homework, please!!

33. Rule:If bases the same set exponents equal to each other

34. 1-6 Radicals (Day 1) and Rational Exponents (Day 2)

35. What is a Radical? In simplest term, it is a square root ( ) = ________________

36. The Principle n th root of a: 1. If a < 0 and n is odd then is a negative number ___________________ If a < 0 and n is even, _____________ __________

37. Vocab

38. Lets Recall

39. Rules of Radicals

40. Practice problems Simplify each expression

41. Class Work problems Simplify each expression

42. 1-6 Radicals (Day 1) and Rational Exponents (Day 2)

43. What is a Rational Exponent? ____________________________________

44. Don’t be overwhelmed by fractions! These problems are not hard, as long as you remember what each letter means. Notice I used “p” as the numerator and “r” as the denominator. p= _____________________________ r= _____________________________ ________________________________________

45. Practice problems Simplify each expression

46. The last part of this topic What is wrong with this number? ___________________________________

47. Rationalizing If you see a single radical in the denominator ______________________________________ ________________________________________

48. Rationalizing If you see 1 or more radicals in a binomial, what can we do?

49. What is a Conjugate? The conjugate of a + b ______. Why? The conjugate _______________________ ___________________________________

50. Rationalizing Multiply top and bottom by the conjugate! Its MAGIC!!

51. 1.7 Fundamental Operations

52. Terms Monomial ______________________________ Binomial _______________________________ Trinomial ______________________________

53. Standard form: _______________________________________ Collecting Like terms

54. F____________ O____________ I ____________ L____________

55. Examples

56. 1-8 Factoring Patterns

57. What is the first step?? _____ Why? __________________________________ ___________________________________

58. Perfect Square Trinomial Factors as

59. Difference of squares

60. Sum/Difference of cubes

61. 3 terms but not a pattern? This is where you use combinations of the first term with combinations of the third term that collect to be the middle term.

62. 4 or more terms? ________________________________________

63. Examples

64. Solve using difference of Squares Solve using sum of cubes

65. Examples of Grouping

67. 1.9 Fundamental Operations What are the Fundamental Operations?

68. Addition, Subtraction, Multiplication and Division We will be applying these fundamental operations to rational expressions. This will all be review. We are working on the little things here.

69. Simplify the following Hint: __________________________________ _______________________________________ 2.What is the domain of problem 1?

73. _______________________________ Lets Watch.

74. Polynomial Long Division

76. 1-10 Introduction to Complex Numbers What is a complex number?

77. To see a complex number we have to first see where it shows up Solve both of these

78. Um, no solution???? does not have a real answer. It has an “imaginary” answer. To define a complex number ____________ ___________________________________ This new variable is “ i “

79. Definition: Note: __________________ So, following this definition: ______________________________

80. And it cycles…. Do you see a pattern yet?

81. What is that pattern? We are looking at the remainder when the power is divided by 4. Why? ___________________________________ Try it with

82. Hints to deal with i 1. __________________________________ 2. __________________________________ ____________________________________ 3._________________________________ ____________________________________

83. Examples

84. OK, so what is a complex number? ______________________________ A complex number comes in the form a + bi

85. Lets try these 4 problems.