Pre-Calculus



Pre-Calculus Name:___________________________

Fall Final Exam Review 2015

Final Exam Notecard: You may use a 3” x 5” note card (both sides) on the final for formulas, notes, and pep talks. It must be handwritten by you and may not have worked out problems, unit circle information, or parent graphs.

Directions: Leave all answers in simplified, exact form unless otherwise stated. Only use a calculator if the problem states that you can. Round all calculator problems to the thousandths.

1. Use the graph to answer the following questions.

a) What is the domain? b) What is the range?

c) For what values of x is [pic] d) Find [pic]

e) Find the x-intercept(s) f) Find the y-intercept

g) If[pic], then x =? h) Is [pic]even, odd, or neither?

i) Is [pic] one-to-one? j) Find all increasing intervals.

k) Find all decreasing intervals. l) Find all constant intervals.

m) Find all local minimum. n) Find all local maximum.

Problems #2-4 require a graphing calculator:

2. A rectangle is inscribed in a circle of radius 3. Let P(x,y) be the point on the circle.

a) Express the area A of the rectangle as a function of x.

b) Express the perimeter P of the rectangle as a function of x.

c) Use your calculator to find the value of x that yields the largest area and state the max area.

d) Use your calculator to find the value of x that yields the largest perimeter and state the max perimeter.

3. A cable company is asked to provide service to a customer whose house is located 2 miles from the road along which a cable is buried. The nearest connection box for the cable is located 5 miles down the road.

a) If the installation cost is $10 per mile along the road and $14 per mile off the road, express the total cost C of installation as a function of the distance x (in miles)

b) Find the cost for x = 1.

c) Use your graphing utility to find the value of x that results in the least cost

and find the least cost.

d) If a person can drive 40mph on the road and 25 miles off road express the

time it takes to get from the cable box to the house as a function of time.

4. Let P (x,y) be a point on the graph of the function at right.

a) Express the distance from p(x,y) to the point (0,2) as a function of x.

b) Use your graphing calculator to find the x value(s) that will minimize the

distance to the point (0,2) and state the minimum distance.

5. Jake has 4000 feet of fence to enclose three sides of a rectangular garden. Find the maximum area of the garden without the use of a calculator.

6. A culture of bacteria obeys the law of uninhibited growth.

a) If 300 bacteria are present initially and there are 800 after 2 hours find k. (Keep k exact)

b) How many will be present in the culture after 5 hours?

c) How long is it until there are 30,000 bacteria? (calculator okay)

7. The half-life of radium is 1690 years. When will a substance have 80% of its radium remaining? (calculator okay)

Find the domain of each function:

8. [pic] 9. [pic] 10. [pic]

Graph. State the domain and range.

11. [pic] 12. [pic] 13. [pic]

14. [pic] 15. [pic] 16. [pic]

17. [pic] 18. [pic] 19. [pic]

Graph by finding all intercepts:

20. [pic] 21. [pic]

Graph the piecewise function:

23. [pic]

Determine algebraically whether each function is even or odd. (#24,25)

24. [pic] 25. [pic]

Accurately graph. Find all intercepts and asymptotes. You may use a non-graphing calculator to help you find points.

27.[pic] 28. [pic]

29. Use your graph from #27 to find each limit: a) [pic] b) [pic] c) [pic]

Evaluate: (Leave answers exact, rationalized and simplified.) No calcs here!

30. [pic] 31. [pic] 32. [pic] 33. [pic]

34. [pic] 35. [pic] 36. [pic] 37. [pic]

38. [pic] 39. [pic] 40. [pic] 41. [pic]

42. [pic] 43. [pic] 44. [pic] 45. [pic]

46. [pic] 47. [pic] 48. [pic]

49. Write as a single logarithm:

a) [pic] b) [pic]

Solve each inequality:

50. a) [pic] b) [pic]

51. Given that [pic] find each function and its domain.

a) [pic] b) [pic] c) [pic] d) [pic] e) [pic]

f) [pic] g) [pic] h) [pic] i) [pic]

no domain no domain .

Solve each equation

52. [pic] 53. [pic] 54. [pic]

55. [pic] 56. [pic] 57. [pic]

58. [pic] 59. [pic] 60. [pic] (calc)

(Leave as a single log and rounded)

Find the domain and range of each trig function.

61.[pic] 62. [pic] 63. [pic]

64. Find the polynomial that has degree 3 and zeros including [pic] and 2. P(0)=100

Find the inverse of each function:

65. [pic] 66. [pic] 67. [pic]

68. How would you restrict the domain of [pic]so that its inverse is also a function?

69. What is true about the graph of [pic]and [pic]when graphed on the same axes?

70. What type of symmetry do even functions have? 71. What type of symmetry do odd functions have?

72. Convert 18° into radians 73. Convert [pic] to degrees

74. Find sinθ and cotθ given [pic] and cscθ*[pic]CJaJhÝv1hÕ2†CJaJ

hÕ2†CJaJ

h`máCJa) Which degree polynomials always have an absolute maximum?

b) Which type of polynomials always have at least one y-intercept?

c) Which type of polynomials never have a range of all real numbers?

26. a) Which trig functions are odd?

b) Which trig functions are even?

Find the domain and range of j(x) and [pic]

[pic]

[pic]

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