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Algebra II Fall Final Exam Review. NAME _________________ Date________________ Period_________________. Part I: Transformations of parent functions. Use the concept of transformations of functions to write the equation from the graph. 7. f(x) = __________________.

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algebra ii fall final exam review

Algebra II Fall Final Exam Review

NAME _________________

Date________________

Period_________________

slide2

.

Part I: Transformations of parent functions

Use the concept of transformations of functions to write the equation from the graph.

7. f(x) = __________________

8. f(x) = __________________

slide3

8. f(x) = __________________

9. f(x) = __________________

Part 2: Determine whether or not the following relations are functions.

10.

slide4

Part 3: State the domain and range for each of the following data.

11.

{(-1, 3) (5, 2) (2, 3) (-1, 2) (4, 3)}

Domain ____________________

Range ____________________

12.

13.

14.

Part 4: Solve the following equations.

15.

16.

18.

6x + 2(3 – x) = 7x + 1

17.

6x – 3(6 – 5x) + 3x = 10 – 4(2 – x)

slide5

Part 4: Continued

Solve for b

Solve for P

19.

20.

21.

22.

23.

24.

25.

3y + 6 < 15 or 1 – 3y < -11

26.

–6 < 4 – 2x < 12

27.

–4y + 8 > 16 or 3y – 5 > 5

slide6

Part 5: Write the equation of the line from the given information.

28.

passing through ( -3, 8) and (5, 4)

29.

passing through ( 2, -4) and (0, 2)

30.

parallel to 2x + y = 10 , passes through (2, -2)

31.

passing through ( -5, 2) with a slope of 3

32.

undefined slope , passes through (4, 2)

33.

Perpendicular to y = -2x – 7 and passes through ( 2, -4)

slide7

Part 6: Determine the slope, x-intercept, y-intercept from the following equations.

34.

8x - 2y = 6

35.

3x + 9y = 18

Part 7: Solve the following systems of equations using the most appropriate method.

36.

x – 4y = 1

-2x + 5y = 4

37.

x + y = 10

3x – 2y = 5

39.

x = -3y + 9

3x + 2y = -1

38.

y =-x + 4

x – 2y = 2

slide8

38.

4x - 2y + z = 2

-x - 3y = - 2z -5

2x = y -3z -4

39.

4x - y + z = 3

x + 2y + z = 0

3x + 7y - 3z = 6

40.

A group of 42 people go to the zoo. The admission price is $6 for adults and $3 for kids. If the group spends $162, how many adults and kids were in the group?

To call London, a long distance phone company charges a fixed rate for the first minute and a different rate for each additional minute. If a 12 minute phone call costs $2.35 and a 25 minute call costs $3.65, how much are their rates?

41.

42.

slide9

Part 8: Determine the inverse of each of the following.

43.

{(2, 3) (4, -1) (5, 1) (-3, -7) (3, -4)}

44.

y = 5 – 8x

46.

45.

47.

48.

slide11

Part 10: Determine the value for the given function.

51.

Part 11: State the domain, range, vertex, axis of symmetry, zeros, and y-intercept.

f(x) = -(x - 5)2 – 3 f(x) = x 2 -15x +56

52.

53.

54.

y = -2 (x -4)2 + 6

slide12

Part 12: Factor each of the following expressions completely.

55.

A. x3 - 2x2 + 8x B .

C. 2x² + 3x + 1 D.

E. 6x² + 12x F. x² + 5x + 6

Part 12: Solve the following quadratic equations by using the quadratic formula.

56.

57.

slide13

Part 13: Graph the following quadratic inequalities.

Write the solution as a conjunction or a disjunction

  • Make a sign graph.

58.

x2 - 2x - 8 > 0

59.

-2x2 + 7x - 4 < 0

f(x) < (x - 3)2 + 1

61.

2x2 - 3x > 2

60.

slide14

Part 14 : Use the laws of exponents to simplify the following

63.

64.

62.

65.

66.

Part 15: Verify that the following functions are inverses.

67.

f(x) = 3x – 6 and g(x) =

x + 6

68.

f(x) = ½ x – 4 and

g(x) = 2x + 8