1. Calculus P - Review Review Problems

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9. Find the points of intersection 8

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28. Review Problems 27

29. Review Problems Given x 2 + x 28

30. Review Problems Find the x-intercept(s): 3x 2 + 2y 2 + 4xy - 12 = 0. ±2 29

31. Review Problems Find the x-intercept(s): y = 2x 2 - 1 30

32. Review Problems Find the x-intercept(s): y = x 3 (x + 2)(3x - 1) (0, 0), (-2, 0), (1/3,0) 31

33. Review Problems Find the intercepts:. (0,-1/3), (1/2,0) 32

34. Review Problems Identify the type(s) of symmetry: x 4 y 2 + 2x 2 y - 1 = 0 To y-axis Identity the type(s) of symmetry: y = x 3 + 3x To origin 33

35. Review Problems Identify the type(s) of symmetry: y = |x| - 2 Symmetric to the y-axis 34

36. Review Problems Determine if is symmetrical with respect to the x-axis, the y-axis, or the origin. About the y-axis 35

37. Review Problems Find all points of intersection of the graphs of x 2 + 3x - y = 3 and x + y = 2 (-5, 7), (1, 1) Find all points of intersection: y = -x 2 + 4x and y = x 2 (0, 0), (2, 4) 36

38. Review Problems Find the number of sales necessary to break even for the cost C of x units and the revenue R obtained by selling x units if C = 3000x + 75000 and R = 3250x 300 37

39. Review Problems If the point (-1, 1) lies on the graph of the equation kx 2 - xy + y 2 = 5, find the value of k 3 38

40. Review Problems Find the slope of the line passing through the points (-1, 16) and (4, 2). Find the slope of a line that is perpendicular to the line given by 2x + 3y + 9 = 0 39

41. Review Problems Find the equation of the line that has a slope of and passes through the point (1, 2). 3x + 4y - 11 = 0 40

42. Review Problems Find the equation of the vertical line that passes through the point (2, 5). x = 2 Find the equation of the line that passes through the point (0, 0) and has a slope that is undefined x = 0 41

43. Review Problems Find the equation of the line that passes through the point (-1, 5) and has a slope of 2 2x - y + 7 = 0 Find an equation for the horizontal line that passes through the point (-3, 2) y = 2 42

44. Review Problems Find the domain:. All reals except 43

45. Review Problems Given f(x) = x2 - 3x + 4, find f(x + 2) - f(2). x 2 + x Given f(x) = |x - 3| - 5, find f(1) - f(5). 0 44

46. Review Problems Find f(x + Δx) for f(x) = x 2 - 2x - 3 x 2 + 2x(Δx) + (Δx) 2 - 2x - 2 Δx - 3 45

47. Review Problems If g(x) = x 2 + 3x - 1, find. 2x + Δx + 3 Find if f(x) = 4x 2 - 2 8x + 4Δx 46

48. Review Problems Which of the following is a sketch of the graph of the function f(x) = x 3 + 1? I 47

49. Review Problems Given the graph of y = x 2, sketch the graph of y = (x + 3) 2 - 1 48

50. Review Problems Use the graph of y = x 2 to find a formula for the function y = f(x). f(x) = (x - 2) 2 + 1 49

51. Review Problems Use the graph of f shown below to sketch the graph of y = f(x) - 2 50

52. Review Problems Describe the transformation needed to sketch the graph of using the graph of Shift f(x) two units upward 51

53. Review Problems Given f(x) = 6x - 12 and g(x) = x 2 - 4, find. 52

54. Review Problems If and find f(g(x)) 53

55. Review Problems If and find f(g(x)) 54

56. Review Problems If f(x) = and g(x) = find g(f( - 2)) 55

57. ANSWERS 1. 2. 3. 4. Graph 5. Graph 6. Graph 7. Graph 8. 9. 10. 11. 12. 13. 14. 15. 16.

58. ANSWERS 17. 18. 19. Graph 20. Graph 21. 22. 23. Graph 24. Graph 25. Graph 26. Graph 27. 28. 29. 30. 31. 32. x 2 + x ±2 (0, 0), (-2, 0), (1/3,0) (0,-1/3), (1/2,0)

59. ANSWERS 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. Graph To y-axis To origin Symmetric to the y-axis About the y-axis (-5, 7), (1, 1)(0, 0), (2, 4) 300 3 3x + 4y - 11 = 0 x = 2x = 0 2x - y + 7 = 0 y = 2 All reals except x 2 + x0 x 2 + 2x(Δx) + (Δx) 2 - 2x - 2 Δx - 3 2x + Δx + 3 8x + 4Δx I

60. ANSWERS 49. 50. Graph 51. 52. 53. 54. 55. 56. f(x) = (x - 2) 2 + 1 Shift f(x) two units upward