B Math is Radical

1. B Math is Radical Pre-Calculus 30

2. PC30.11 • Demonstrate understanding of radical and rational functions with restrictions on the domain.

3. Key Terms

5. 1. Radical Transformations • PC30.11 • Demonstrate understanding of radical and rational functions with restrictions on the domain.

6. 1. Radical Transformations • The base radical function you have seen before. It is

7. The graph of has the following properties: • x-intercept of 0 • y-intercept of 0 • Domain: x≥0, xЄR • Range: y≥0, yЄR • The intercepts and domain and range suggest an endpoint of (0,0) and no right end point • The graph is shaped like half a parabola. The domain and range indicate that the half parabola is in the first quadrant

8. Transforming a Rational Function: • The base radical function is transformed by changing the values of the parameters a, b, h, and k in the equation • The parameters have the same effects on the base function as we saw in the last unit.

9. a or : • Vertical stretch by a factor of IaI or • If a<0, the graph is reflected in the x-axis • or a: • Vertical stretch by a factor of IbIor • If b<0, the graph is reflected in the y-axis

10. h: • Horizontal translation • (x-h) means we move h units to the right. • (x+h) means we move h units to the left. • (opposite of what you would think) • k: • Vertical translation • - k means we move kunits down. • +k means we move kunits up.

11. Example 1

12. Example 2

13. Example 3

14. Example 4

15. Key Ideas p.72

16. Practice • Ex. 2.1 (p.72) #1-5 odds in each, 6-13 # 1-5 odds in each, 6, 7-19 odds

17. 2. Root Functions • PC30.11 • Demonstrate understanding of radical and rational functions with restrictions on the domain.

18. We can use the graph of the easier looking function to graph the function • To graph , you can set up a table of values for the graph . Then, take the square root of the elements in the range, while keeping the elements in the domain the same

19. When graphing , pay special attention to the invariant points. • The invariant points are (x,0) and (x,1) because when =0, , when =1,

20. Domain and Range of : • You cannot take the square root of a negative number, so the Domain of is a any value for which • The Range is the square root of any value in for which is defined.

21. Things to keep in mind when graphing : • If • is undefined because you cannot take the square root of a negative. • If • and intersect at x-axis

22. If • is above • If • and intersect • If • is below

24. Example 1

25. Example 2

26. Example 3

27. Key Ideas p. 85

28. Practice • Ex. 2.2 (p.86) #1-4, 5-8 odds in each, 9-13 odds #5-8 odds in each, 9-19 odds

29. 3. Solving Radical Equations • PC30.11 • Demonstrate understanding of radical and rational functions with restrictions on the domain.

30. 3. Solving Radical Equations • Investigate p.90

31. Remember back to last year. We have solved radical equations already. That is what you were doing in the investigation. • If you recall there were two way we solve radical equations. Graphically and Algebraically. We will quickly review each method.

32. Strategy to solve Algebraically: • List all restrictions on the variable. • Isolate the radical and square both sides of the equation to eliminate the radical. • Solve for x (find the roots/zeros). • Check the solutions by subbing into the equation and by checking your restrictions. For example:

33. To solve Graphically there are two methods:

34. Method 1: Graph the corresponding function and find the zero(s) of the function. For example: Graph:

35. Method 2: Graph each side of the equation on the same grid, and find the intersection point(s). For example: Graph:

36. What is the relationship between the roots of an equation and the x-intercepts of the graph?

37. Example 1

38. Example 2

39. Example 3

40. Key Ideas p.96

41. Practice • Ex. 2.3 (p.96) #1-8 questions with 4 parts do 2, 9-14 # 1-8 questions with 4 parts do 2, 9-17 odds