1. Reviewing Properties of Exponents Exponentiation is repeated Multiplication: To get to each succeeding line, divide by a: a 4 = a × a × a × a a 3 = a × a × a a 2 = a × a a 1 = a a 0 = 1 a -1 = 1/a a -2 = 1/a 2 a -3 = 1/a 3

2. Rules of Exponents

3. Try These

4. Roots and Radical Expressions

5. Some Exercises using Radicals TEXT: Page 365:27, 28, 35, 36, 37

6. Some Properties of Radicals

7. Express the Following in Simplest Form

8. How Can we Simplify this expression keeping with the Radical notation?

9. HWK 26 Text: Page 360: 16, 18, Page 365: 38, 40, 42 Page 371: 14, 26, 36, 40, 48

10. Binomial Radical Expressions

11. Simplify the Following Expressions

12. Simplify These

13. Another Notation: Rational Exponents

14. Examples

15. HWK 27 Express all answers in simplified form. Page 378-380: 16, 36, 37, 51, 64, 66 Pages 386-390: 62, 92, 96, 97

16. Solving Radical Equations  Method is similar to what we did with absolute value equations. Follow these Steps: 1)Isolate Radical; Rational exponent notation may be useful 2)Raise both sides to a power so that unknown will no longer be a radicand. 3)Raising radicals to powers can introduce extraneous solutions. Always check final answers in the original equation.

17. Solve the Following

18. Solving Equations with Two Radicals

19. HWK 28 Hwk 28 A2T text: Due Thursday 2/11 Page 372: 54, 55 Pages 395-397: 16, 22, 28, 40, 64 Hwk 28 A2T text: Due Thursday 2/11 Page 372: 54, 55 Pages 395-397: 16, 22, 28, 40, 64 Hwk 28 A2T text: Due Thursday 2/11 Page 372: 54, 55 Pages 395-397: 16, 22, 28, 40, 64

20. Function Operations

21. Some Examples

22. Composite Functions

23. Some Examples

24. More Examples 2)You have a coupon for $5 off a pizza and a student ID which gives you 10% off any pizza. Which results in a cheaper price; applying the coupon then the discount, or vice-versa?

25. Another Example 3)A store offers a 15% discount on all items and a 20% discount to store employees. a)Write a model for the price found by taking off the 15% discount before the 20% discount. b)Write a model for the price found by taking off the 20% discount before the 15% discount. c)Which results in a cheaper price?

26. Inverting Relations and Functions If (a,b) is an ordered pair of a relation, then (b,a) is an ordered pair of the relation’s inverse. If both a relation and its inverse are functions, then they are “inverse functions”. The range of a relation is the domain of its inverse. The domain of a relation is the range of its inverse. The inverse of a function is not necessarily a function : domainrange 11.2 11.4 21.6 21.9 domainrange 1.21 1.41 1.62 1.92 A function -> Inverse is NOT a function ->

27. How Can We Invert a Relation?

28. Notation for the Inverse of a Function The inverse of a function f denoted by f -1. (Note: f -1 may not be a function). Where have we seen this notation before to denote the inverse of something?

29. Example

31. Inverse of a Formula

32. One to One Functions

33. Composing Inverse Functions

34. Graphing and Transforming Radical Functions General Transformations. From a parent function: f(x) we can form the following transformation: g(x) = a f(x-h) + k where, the parent function has been:  shifted to the right by h THEN  scaled by |a| and reflected across the x-axis if a<0 THEN  shifted up by k.

35. Does Order Matter? Consider f(x) = x 2 and consider the following two series of transformations: 1)Shift to the right by 2, stretch by 3, then shift by 4. a)Shifting right gives: g 1 (x) = f(x-2) = (x-2) 2 b)Stretch by 3 gives: g 2 (x) = 3g 1 (x) = 3(x-2) 2 c)Shift up by 4 gives: g 3 (x) = g 2 (x)+4 = 3(x-2) 2 +4 2)Shift to right by 2, shift up by 4, then stretch by 3. a)Shifting right gives: g 1 (x) = f(x-2) = (x-2) 2 b)Shift up by 4 gives: g 2 (x) = g 1 (x)+4 = (x-2) 2 +4 c)Stretch by 3 gives: g 3 (x) = 3g 2 (x)= 3(x-2) 2 + 12 So: Yes; Pay attention to the order. Each successive transformation acts on the entire function generated by the previous transformation.

36. Examples

37. Solve by Graphing

38. HWK 31 Due Tuesday 2/24: Page 419: 53 (to be done in class and added to hwk 31 for grading.) Pages 418-419: 36, 44, 48, 54