1. Chapter 8 Irrational Roots Clark/Anfinson

2. CHAPTER 8 – SECTION 1 Root functions

3. Investigating a function

4. Graph

5. What the graphs tell us Even roots domain is restricted Range is restricted generally increasing Negatives cause decreasing behavior Not a constant rate of increase or decrease Odd root Domain is not restricted Range is not restricted generally increasing Negatives cause decreasing behavior Not a constant rate of increase or decrease

6. Finding domain and range

7. Domain and range continued

8. Answering f(x) questions using graph Use the graph to find f(4), f(6) and f(-3) Use the graph to find where f(x) = 2, f(x) = 3.5

9. CHAPTER 8 - SECTION 2 Simplify/add-subtract irrational roots

10. Irrational numbers

11. Simplifying radicals A radical is considered simplified when there are no factors within the radical that are higher powers than the root. ie. If the root is 2 there are NO powers inside the radical if the root is 3 there are no square powers inside the radical

13. Addition and radicals

14. Examples

15. Simplify radicals BEFORE you add

16. CHAPTER 8 – SECTION 3 Multiplying/dividing radicals

17. 2 variations on rule

18. Examples

19. Multiplication with addition

20. Division with radicals

21. CHAPTER 8 – SECTION 4 Solving radical equations

22. Solving – isolate the variable by inversing You can do ANYTHING to an equation as long as you change both SIDES the same way. Anything includes inserting and exponent on the WHOLE side

23. Example

24. How restrictions affect solving

25. CHAPTER 8 – SECTION 5 Imaginary numbers

26. Definition

27. Examples

28. Simplifying Complex numbers