Advanced Algebra 2 Chapter 6 Review PDF

ADVANCED ALGEBRA 2 NAME: _______________________________________ Review-Chapter 6 Rewrite each of the following in radical form. 6.1 1. 31/2 2. x3/5 3. 164/3...

ADVANCED ALGEBRA 2 NAME: _______________________________________ Review-Chapter 6 Rewrite each of the following in radical form. 6.1 1. 31/2 2. x3/5 3. 164/3 I can definitely do this on my own. Rewrite each of the following using exponents. ! I can do this with a ! " 4. √9 5. #√10& 6. √20! little help. Evaluate without using a calculator. I need a lot of help to # ! do this. 7. √64 8. 253/2 9. √125 I am really struggling. Simplify the expression. Make sure all answers have positive exponents. 6.4 "# I can definitely do ! "/$ 10. (2x1/4)(3x3/4y)(4y-1/3) 11. ! " this on my own. ! $/% I can do this with a little help. I need a lot of help to -1/2 do this. æ x1/2 y1/3 ö 12. (-27x y ) 4 5 -1/3 13. ç 1/3 2/3 ÷ èx y ø I am really struggling. 6.3 14. √6(√7 − 3√2) 15. (5 + √3)(6 − √5) I can definitely do this on my own. I can do this with a little help. (%"√#) 16. (("√#) I need a lot of help to do this. I am really struggling.  6.2 Simplify the given radical. I can definitely do ! $ 17. √320 18. 3 √486 19. 3√4 ∙ 4√8 this on my own. I can do this with a little help. I need a lot of help to ! " 20. √54𝑎& 21. /81𝑥 ! 𝑦 & 𝑧 ' 22. /24𝑥 ! 𝑦 ( do this. I am really struggling. Simplify the given radical. Be sure to rationalize the denominator. 6.2 ) % % (! 23. # 24. #* I can definitely do ) this on my own. I can do this with a little help. I need a lot of help to do this. % % * 25. #(+,$ -* I am really struggling. %+ , Simplify each of the following radical expressions. 6.3 ! ! 26. 2√3 + 9√3 + 3√4 27. 3 √5 − 3√135 I can definitely do this on my own. I can do this with a little help. I need a lot of help to 28. 2/9𝑥 + 𝑦 , + 5𝑥𝑦/16𝑦 ! ! 29. 4𝑎 √𝑏- − 7𝑏 √𝑎! 𝑏. ! do this. I am really struggling. Simplify each of the following radical expressions. 6.6 f(x) = 2x + 1 g(x) = 7x – 9 I can definitely do this on my own. 30. Find (f + g)(x). 31. Find (g – f)(x). I can do this with a I need a lot of help to do this. I am really struggling. 32. Find (fg)(x). 33. Find (fg)(-3). Use the functions below for questions 5 – 8. Also state the domain when necessary. f(x) = 3x-5 g(x) = -12x3 34. Find (fg)(x). 35. Find (f/g)(x). 36. Find (g/f)(x). 37. Find (f/g)(2). Use the functions below for questions 35 – 37. f(x) = x + 1 g(x) = x2 + 3x – 4 38. Find f(g(3)). 39. Find f(g(x)). 40. Find g(f(x)). Solve each equation. Check for extraneous solutions. Write answers in simplest radical form. 6.5 41. 2𝑥 ! + 36 = 100 42. 2(𝑥 − 3)" − 12 = 50 I can definitely do this on my own. I can do this with a little help. I need a lot of help to do this. I am really struggling. " 43. −4√𝑥 + 2 − 1 = 7 44. 7 − √𝑥 − 4 = −6 45. (8x)4/3 + 44 = 300 46. (x – 5)5/3 – 73 = 170 47. 𝑥 + 2 = √2𝑥 + 7 Find the inverse of the function. 48. f(x) = 2x – 13 49. g(x) = 2x3 – 3 6.7 I can definitely do Tell whether the function graphed below has an inverse function. this on my own. 50. I can do this with a little help. I need a lot of help to do this. I am really struggling. Verify that the functions provided are inverses. !"# 51. f(x) = 3x – 4; g(x) = 52. f(x) = √𝑥 − 4 + 1; g(x) = (x – 1)2 + 4 $ Graph the function. Give the domain and range. Label your axes with appropriate 6.8 scale. I can definitely do ! 53. f(x) = 2 √𝑥 + 1 this on my own. I can do this with a little help. I need a lot of help to do this. I am really struggling. 54. g(x) = √𝑥 + 1 ! 55. Let the graph of g be a vertical stretch by a factor of 2, followed by a translation 3 units left of the graph of f(x) = √𝑥. Write a rule for g. 56. Let the graph of g be a horizontal shrink by a factor of ½, followed by a reflection in the x-axis and a vertical translation up 6 of the graph of f(x) = √𝑥 + 2. Write a rule for g. / 57. Describe the transformation of f(x) = √𝑥 represented by g(x) = − √𝑥 − 3 + 1. !