2. Is the graph a function or a relation? Function Relation

3. State the domain of the function: All real numbers except 1 or -1 All real numbers except 3 or -3 All real numbers except 5 All real numbers except 0 and 5

4. Find the composition functions below:

5. Find the x- and y- intercepts: (12,0) and (0,6)(6,0) and (0,-4)

6. Find the zero of each function:

7. Dominic is opening a bank. He determined that he will need $22,000 to buy a building and supplies to start. He expects expenses for each following month to be $12,300. Write an equation that models the total expense y after x months.

8. Determine whether the graphs of the pair of equations are parallel, coinciding, or neither. x - 2y = 12 and 4x + y = 203x - 2y = -6 and 6x - 4y = -12 NeitherCoinciding

9. Write an equation of the line that passes through the points given: (-2,4) and (6,-4)(3,-5) and (0,4)

10. Write an equation of a line using the information given. 1. No slope, (3,4)2. slope = 3, (-3, -7) Slope is undefined VERTICAL LINE

11. How can you tell if two lines are perpendicular?  Their slopes are opposite reciprocals  HOW CAN WE TELL IF THEY ARE PARALLEL?  Their slopes are the SAME

12. Given f(x) and g(x), find (f/g)(x)

13. Solve this system of three variables:

14. Find the product of each: DOES NOT EXIST 2X3 2X2

15. Evaluate the determinant of this 3x3 matrix: 1-2 3 0 -7 1 DOWNHILL - UPHILL (0+56+12)- (0+4-18) 68 – (-14) 82 (18+280+0)- (0+0-8) 3-4 1 3 -10 0 246+8 254

16. Evaluate each function given: 1. f(a 2 ) 2. f(3b 4 )

17. Graph each function: 1. f(x) = 3x – 4 2. f(x) = - ⅔ x + 1

18. Find the values of x and y for which the matrix equation is true. I would use substitution:

19. Given the two matrices, perform the following operations. A = B = 1. 3B 2. 2A - C Impossible

20. Find the inverse of each matrix. 1. 2. Does not exist

21. Graph each inequality: 1. 2x + y – 3 < 02. x + 3y – 6 ≥ 0

22. Determine the intervals of increasing and decreasing for each function: Decreasing x < 1 Increasing x > 1 Decreasing -1.5 < x < 0.2 Increasing x 0.2

23. a. c.  5 b.  2 d. Use the possible rational zeros theorem to determine which number cannot be a zero of P(x) = 10x 4 + 6x 2 – 5x + 2.

24. What lines are symmetric to each function given: 1. 2. x = 0 y = 0 x = 4 y = -2

25. Graph each function and it’s inverse. 1. 2. f(x) f -1 (x) f(x) f -1 (x)

26. a. Increasing for all x c. Decreasing for all x b. Increasing for x > 0 d. Decreasing for all x < 0 Determine the interval on which the function is increasing.

27. a. between  1 and 0 c. between 1 and 2 b. between 0 and 1 d. between 2 and 3 For f(x) =  2x 4 + 3, use the intermediate value theorem to determine which interval contains a zero of f.

28. Determine whether the critical pt given is a max, min, or pt of inflection. 1. x = 0 2. x = 1 MAX MIN

29. Approximate the real zero. 1. 2. x y -5 -65 -4 -25 -3 -5 -2 1 0 -5 1 -5 2 5 3 31 x y -5 435 -4 138 -3 19 -2 -6 -1 3 0 10 1 3 2 -6 3 19 So there is zeroes between - 3 and -2, - 2 and -1, 1 and 2 Rule of thumb: go from -5 to 5 for your x-values If they want a decimal approximation, you need to make another t-chart going by 0.1 in between these approximated zeros. Or you could just plug each answer and see which one gets you closest to a ZERO

30. Solve the system of inequalities by graphing

31. Use the related function to find the min and max. 1. 2.

32. Determine the vertical asymptotes of each function VA: x = 0 VA: x = ⅓ VA: x = 4, x = 0

33. Graph each rational function Hole at x = -2 Hole at x = 0

34. Find the roots of: A.) B.) C.) 2, -1 D.) -2, 1 USE THE COMMON ROOT AND DO SYNTHETIC DIVISION FIRST 2 IS COMMON AMONG ALL THE ANSWERS AFTER SYNTHETIC DIVISION, TRY TO FACTOR, OR QUADRATIC FORMULA TO FIND THE REST OF THE ROOTS.

35. Find the number of positive, negative, and imaginary roots possible for this function: 3, 1 positive roots 0 Negative roots P N I 3 0 2 1 0 4 Each row adds up to degree of polynomial In a polynomial equation, if there is four changes in signs of the coefficients of the terms, __________________________ there is 3 or 1 positive roots

36. Using Law of Sines 1.In ΔABC if A = 63.17°, b = 18, and a = 17, find B 2. In ΔABC if A = 29.17°, B = 62.3°, and c = 11.5, find a

37. Determine the type of discontinuity for each function: Infinite Dis.Jump Dis.Point Dis.

38. Find the maximum value for this system of inequatilites: Unbounded SolutionInfeasible Solution Optimal Solution Graph the system first, you might get one of these three options.

39. Solve this rational inequality: Need to do a number line and test around 0, -2, and 2 -2 0 2 NO YES NOYES Solution:

40. Which graph represents the polynomial a.b. c.d. function

41. Evaluate each problems using the unit circle:

42. Determine for each function if it is odd, even, or neither? Odd functions are symmetric with respect to the origin: (a,b) and (-a,-b) Even functions are symmetric with respect to the y-axis: (a,b) and (-a,b) EVEN BOTH ORIGIN EVEN

43. List all possible rational roots of each function: P: 1, 2, 5, 10 Q: 1 P: 1,3 Q: 1, 2, 4

44. Convert 220º to radian measure in terms of π.

45. Solve triangle ABC to find b. a. 3.6 m c. 5.2 m b. 13.1 m d. No solution a = 10 m, B = 14º, C = 28º

46. Use the triangles below to find missing cos A, sin A, tan A A 8 ft. 5 ft.

47. Solve triangle ABC to find A. a. 8.5º c. 81.5º b. 87.9º d. No solution a = 12.5 in., b = 10.5 in., c = 8.5 in.

48. Given thatand that the terminal side is in quadrant III, find sin .

49. Find a. 120º c. 150º b. –60º d. 30º exactly in degrees.

50. a. c. 2π b. π d. 4π For the function find the period.

51. Given right triangle ABC with a = 16.5 and A = 23.5º, find c. Standard lettering has been used. a. 18.0 c. 15.1 b. 41.4 d. 6.6

52. Use the unit circle to find each: 0 undefined

53. Given the triangle, find cos .

54. State the amplitude for each function: Amplitude = noneAmplitude = 2 Amplitude = 1

55. Find the exact function value, if it exists, of

56. Find the period for each function: Period = π/k = πPeriod = 2π/k = 2π/3 or 120° Period = 2π/k = 6π or 1080°

57. Graph each function VA: x = -3 HA: y = 0 VA: x = 5 HA: y = 0