1. Pre-Calculus 1 st Semester Final Exam Review, Day 1 1. Write an equation to match the graph: 2. What is the domain of the function that represents the graph? 3. What is the range of the function?

2. 4. Write an equation to match the graph shown. 5. What is the domain of the function that represents the graph? 6. What is the range of the function?

3. 7. The value of a car after t years is determined by the model: y = 35,000 – 5000t. Graph the function on your calculator. Change the window settings to best fit the graph. Sketch the graph of the function here:

4. 8. Find an equation for a line that passes through the points (–1, 6) and (11, –6). 9. Find an equation for a line that passes through (1, 2) and is perpendicular to the line above.

5. 10. Radio advertising in the US totaled $3.7 million in 2004, and totaled $7.4 million in 2012.If this trend continues as a linear pattern, predict the total for this year. 11. The ground floor of the ‘A’ building is 4 meters. Each floor above adds 3 meters per floor. Write an equation that expresses the height h of the building as a function of x the number of floors.

6. 12. Use a graphing utility to approximate the solution(s) of x 3 – x + 9 = 0. 13. Given the piece-wise function:, find f(–2). 14. Prove algebraically if the following function is odd, even, or neither: f(x) = 2x 3 + 3x 2

7. Pre-Calculus 1 st Semester Final Exam Review, Day 2 15. Write an equation for the graph shown, that describes the transformation of f(x) = |x| 16. Sketch the graph of the function f(x) = ½(x + 3) 2 – 1, by hand.

8. 17. Given f(x) = 9x + 1, and g(x) = 4 – x, find (f – g)(x). 18. Given f(x) = x 2, and g(x) =, find (f g)(x). 19. Given f(x) =, find f –1 (x).

9. 20. Determine the left and right behavior of the graph: f(x) = 3x 5 – 7x 2 + 2. 21. Find all the real zeros of f(x) = x 3 – 3x 2 – 4x 22. Find all the real zeros of f(x) = 3x 4 – 27x 3 + 54x 2

10. 23. Find a polynomial function with the zeros: 1, 0, –3 24. Multiply: (3 + 7i). (6 – 2i) 25. Find a 4 th degree polynomial function with the zeros: 1, –3, 2i. 26. Completely factor: f(x) = x 4 – 16.

11. Questions 27,28: Find the vertical and horizontal asymptote(s), and sketch: 27. 28.

12. 29. Find the domain:

13. Pre-Calculus 1 st Semester Final Exam Review, Day3: 30. Convert to radians: 240° 31. Convert to degrees: 32. Find the angle complementary to. 33. Find the exact value of sec π. 34. Find the exact value of tan. 35. Using the right triangle, find the exact value cot θ. 7 4 θ

14. 36. Find an angle less than, where sin θ = 37. Determine which quadrant(s), where tan θ < 1. 38. If cos θ = –, find the value of tan θ.

15. Questions 39,40: Write equations for the following functions: 39. 40.

16. 41. Sketch: y = 4. sin 4x 42. Sketch: y = tan ½x

17. Pre-Calculus 1 st Semester Final Exam Review, Day 4 43. Sketch: y = 2. csc πx 44. Sketch: y = sin (x – )

18. 45. Evaluate: arcsin. 46. Evaluate: arccos. 47. Evaluate: sin(arccos. 48. Evaluate: sin(arctan ).

19. 49. A ladder is leaning against the side of a house. The base of the ladder is 5 ft from the wall, and the ladder makes an angle of 39° with the ground. What is the length of the ladder? 50. If csc x = –3, what are possible values of cos x?

20. 51. Simplify: 52. Simplify:

21. 52. Verify: 54. Find all the solutions in the interval [0, 2π): 2cos x + 1 = 0