Algebra 2 module 5

Algebra 2 module 5 5.15 1. (01.01) Anna and Belle are asked to solve –2x – 15 = 6x + 9. Identify where one of them made an error. Anna Belle –2x – 15 = 6x + 9 –2x – 15 –6x = 6x + 9 –6x –8x – 15 = 9 –8x – 15 + 15 = 9 + 15 –8x = 24 x = –3 –2x – 15 = 6x + 9 –2x – 15 + 2x = 6x + 9 + 2x –15 = 8x + 9 –15 + 9 = 8x + 9 + 9 –6 = 8x (1 point) Anna made the error when she subtracted 6x. Anna made the error when she divided by –8. Belle made the error when she added 2x. Belle made the error when she added 9. 2. (01.02) The function for the cost of materials to make a biscuit is f(x) =   x + 4, where x is the number of biscuits. The function for the selling price of those biscuits is g(f(x)), where g(x) = 4x + 5. Find the selling price of 15 biscuits. (1 point) 16 56 65 69 3. (01.02) Given the function f(x) =   , which of the below expressions is correct? (1 point) f–1(x) = f–1(x) = f–1(x) = f–1(x) = 4. (01.04) Carl has been recording the number of pears on his pear tree each week: Week Pears 6 32 7 37 8 42 9 47 The function representing Carl's pears per week is f(w) = 5w + 2. What does the 2 represent? (1 point) The week number when Carl recorded the pears The number of pears at the start The number of pears Carl had in total The number the pears increased by each week 5. (01.04) Based on the table of values below, find the slope between points where x = 2 and where x = 6. x y 2 12 4 10 6 4 (1 point) –3 –2 –1 6. (01.05) A function is created to represent the amount of money in your checking account. What restrictions would be made to the domain? (1 point) The domain would include all real numbers. The domain would only include positive integers. The domain would only include positive numbers. The domain would only include integers. 7. (01.05) To which graph does the point (2, 4) belong? (1 point) y= x + 3 y= –x + 8 y= 4x – 5 y= –2x + 9 8. (01.05) What is the standard form equation of the line shown below? (1 point) y + 3 = –2(x – 1) y = –2x – 1 2x + y = –1 –2x – y = 1 9. (01.06) Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= 3x – 3 (1 point) The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the same slope. The relationship between slopes cannot be determined. 10. (01.06) Ella runs a cat rescue center. She started with 2 cats, and her center has an increase of 5 cats per year. Which of the graphs below represents the number of cats per year at Ella's center? (1 point) 11. (02.01) What is the simplified form of   ? (1 point) 12. (02.01) Which of the following represents   in radical form? (1 point) 13. (02.02) Simplify   . (1 point) 14. (02.02) Simplify   . (1 point) –4 4 15. (02.03) Find the solution of   and determine if it is an extraneous solution. (1 point) x = 1; not extraneous x = 1; extraneous x = 29; extraneous x = 29; not extraneous 16. (02.05) Which of the following expressions is the conjugate of a complex number with –5 as the real part and 4i as the imaginary part? (1 point) 5 + 4i 5 – 4i –5 – 4i –5 + 4i 17. (02.06) Simplify (–8 + 8i) – (5 + 4i). (1 point) –17 –9 –13 + 12i –13 + 4i 18. (02.07) Classify the expression 7x3 as a monomial, binomial, trinomial, or polynomial. (1 point) Monomial Binomial Trinomial Polynomial 19. (02.08) Simplify (4x2+ 12x - 9) + (7x2- x + 3). (1 point) 11x2+ 12x - 6 11x2+ 13x + 6 11x2+ 11x + 6 11x2+ 11x - 6 20. (02.08) Braxton and Maggie babysit children for extra money over the summer. Braxton's income is determined by f(x) = 9x + 10, where x is the number of hours. Maggie's income is g(x) = 6x + 15. If Braxton and Maggie were to combine their efforts, their income would be h(x) = f(x) + g(x). Assume Braxton works 5 hours. Create the function h(x) and indicate if Braxton will make more money working alone or by teaming with Maggie. (1 point) h(x) = 15x + 25, work alone h(x) = 3x + 5, work alone h(x) = 3x + 5, team with Maggie h(x) = 15x + 25, team with Maggie 21. (03.01) Factor completely 81x2– 100. (1 point) (10x – 9)(10x – 9) (10x – 9)(10x + 9) (9x – 10)(9x + 10) (9x – 10)(9x – 10) 22. (03.02) What is the factored form of 5x2 + 28x + 15? (1 point) (5x + 3)(x + 5) (5x + 2)(x + 1) (5x – 5)(x + 4) (5x + 1)(x– 4) 23. (03.04) What is the axis of symmetry for f(x) = –3x2 + 18x – 7? (1 point) x = –3 x = 3 x = –6 x = 6 24. (03.04) The graph of f(x) = x2 has been shifted into the form f(x) = (x – h)2 + k: What is the value of h? (1 point) –3 –2 2 3 25. (03.04) What is the axis of symmetry for f(x) = 2x2 + 8x + 8? (1 point) x = –2 x = –4 x = 4 x = 2 26. (03.04) Use the graph below for this question: What is the average rate of change from x = 0 to x = 2? (1 point) – 4 – 8 1 5 27. (03.06) Which of the following is a solution of x2 + 6x = –18? (1 point) x = 3 – 3i x = –3 + 3i x = –6 + 3i x = 6 – 3i 28. (03.07) Solve 2x2 – 3x + 6 = 0. (1 point) 29. (03.07) Solve x2 + 4x + 1 = 0. (1 point) 30. (03.07) Which of the following is a solution of x2 + 2x + 8? (1 point) 4 + –1 + 2 + –4 + 31. (03.08) Solve3x2 + 4x = –5. (1 point) 32. (03.09) What is the equation of the quadratic graph with a focus of (8, –8) and a directrix of y = –6? (1 point) f(x) = –   (x – 7)2 + 1 f(x) = –   (x – 8)2 f(x) = –   (x – 8)2 – 7 f(x) =   (x – 7)2 33. (04.01) What is the quotient (91y3 + 21y2 - 35y) ÷ 7y? (1 point) 13y2 - 3y - 3 13y2 - 3y + 5 13y3 + 3y2 - 5y 13y2 + 3y - 5 34. (04.02) What is the remainder when (3x4 + 2x3 - x2 + 2x - 19) ÷ (x + 2)? (1 point) 0 5 10 15 35. (04.03) What are the zeros of the polynomial function f(x) = x3 + 2x2 - 24x? (1 point) -6, 0, 4 6, 0, -4 -6, 0, -4 6, 0, 4 36. (04.04) What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 + 5x3 - x2 + 8x + 4? (1 point) Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0 Positive: 1; negative: 3 or 1; complex: 2 or 0 Positive: 3 or 1; negative: 1; complex: 2 or 0 Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0 37. (04.05) Which of the following represents the zeros of f(x) = 6x3 - 35x2 + 26x - 5? (1 point) -5,   , 5, -   , 5,   , - 5,   , 38. (04.07) What are the coordinates of the turning point for the function f(x) = (x - 1)3 - 3? (1 point) (-1, -3) (-1, 3) (1, -3) (1, 3) 39. (04.07) Use the table of the function f(x) = x4 - 4x to answer this question: x f(x) -2 24 -1 5 0 0 1 -3 2 8 What is the average rate of change from x = -1 to x = 2? (1 point) -3 -1 1 3 40. (04.07) Which of the following graphs represents the function f(x) = x2 + x - 6? (1 point) 41. (04.07) Given the parent function of f(x) = x3, what change will occur when the function is changed to f(x + 3)? (1 point) Shift to the right 3 units Shift to the left 3 units Shift up 3 units Shift down 3 units 42. (04.08) What polynomial identity should be used to prove that 21 = 25 - 4? (1 point) Difference of Cubes Difference of Squares Square of Binomial Sum of Cubes 43. (05.01) What is the simplified form of   ? (1 point) 44. (05.02) What is the simplified form of   ÷   ? (1 point) 45. (05.03) What is the simplified form of   +   ? (1 point) 46. (05.04) What is the simplified form of   ? (1 point) 47. (05.06) What is the graph of the function f(x) =   ? (1 point) 48. (05.07) What is the graph of the function f(x) =   ? (1 point) 49. Solve   for x and determine if the solution is extraneous or not. (1 point) x = -2, extraneous x = -2, non-extraneous x = 2, extraneous x = 2, non-extraneous 50. (05.08) Solve   for x and determine if the solution is extraneous or not. (1 point) x = -6, extraneous x = -6, non-extraneous x = 6, non-extraneous x = 6, extraneous 51. (05.09) Two mechanics, Martin and Gordon, are working on your car. Martin can complete the work in 4 hours, while Gordon can complete the work in 2 hours. How many hours does the maintenance take if they work together? (1 point)