Math 1111 Final Exam Review PDF

Preview

Summary

Review for finals...

Description

Student:_____________________ Date:_____________________ 1. Solvetheequation. 6(x + 5) = 7[x − (3 − x)]

A.

−

51

51

B.



8 15

C.



4

D.

−



8

15



4

2. Solvetheequation. 3x + 5 3

8

+

A.

3

−

= −

5 7

5

B.

−

D.

−

5





7

C.

2x

65  9 65



21

3. Solvetheequation. 5−x x

+

3 4

=

7 x

A. { − 8} B. { − 4} C.

−

D. {8}

8 7



Instructor:LisaYocco Assignment:Math1111FinalExam Course:Math1111SCYoccoFall2016 Review

4. Solvetheequationbyfactoring. 2

18x + 14x = 0 A. {0} B. C. D.

7 9 7 9

,0 ,− 7

−

9

7 9

,0

5. Solvetheequationbyfactoring. 2

5x − 75 = 0 A.

−

15 , 15

B. {37.5} C.

15

D. {16} 6. Solvetheequationbyfactoring. 2

12x − 5x − 25 = 0

A. B.

5 5 , 4 3

− 5 4

,−

C.

5 5 , 4 3

D.

−

5 4

5 3

,−

5 3

7. SolvetheequationbytheSquareRootMethod. 2

x = 64 A. {8, − 8} B. {32} C. {9, − 9} D. {8}

8. Findtherealsolutions,ifany,oftheequation.Usethequadraticformula. 2

x − 4x − 13 = 0 A.

−2+

B.

4+

17 ,4 −

17

C.

2+

17 ,2 −

17

D.

2+

13 ,2 −

13

17 , − 2 −

17

9. Findtherealsolutions,ifany,oftheequation.Usethequadraticformula. 2

6x + 8x = − 1

A.

B.

C.

D.

−4−

10 − 4 + 10 , 6 6

−4−

22 − 4 + 22 , 6 6

−8− 6 −4− 12

10 − 8 + 10 , 6 10 − 4 + 10 , 12

10. Writetheexpressioninthestandardforma + bi. (7 + 7 ) − ( − 4 + ) A. 11 − 6 B. 11 + 6 C. 3 + 8 D.

− 11 − 6

11. Writetheexpressioninthestandardforma + bi. ( − 5 + 4 )(2 + ) A.

− 14 − 13

B.

− 6 − 13

C.

− 14 + 3

D.

−6+3

12. Writetheexpressioninthestandardforma + bi. 6+8 6−2

A. B.

13

−

8 1

−

32

3 32 3 32

C. 26 − 18 D.

1 2

+

3 2

13. Performtheindicatedoperationsandexpressyouranswerintheforma + bi. − 81 A. 9 B.

−9

C.

±9

D.

9

14. Findtherealsolutionsoftheequation. 8x + 9 = 9 A. {81} B.

45 4

C. {9} D.

81 8

15. Findtherealsolutionsoftheequation. x = 12 x A. {0,144} B. {0,12} C. { − 12,12} D. { − 144,144}

16. Findtherealsolutionsoftheequation. 26x − 13 = x + 6 A. { − 6} B. { − 7} C. {9} D. {7} 17. Findtherealsolutionsoftheequation. 4

2

x − 5x + 4 = 0 A. { − 1,1, − 2,2} B. { − 5,5} C. { − 2,2} D. { − 4,4} 18. Findtherealsolutionsoftheequation. 4

2

3x + 13x − 10 = 0 A. { − 5,5} B.

−

C.

−

D.

−

2 3

,

2 3

2 2 , 3 3 5 3

,

5 3

19. Findtherealsolutionsoftheequationbyfactoring. 3

x − 64x = 0 A. {0,64} B. {0, − 8} C. {0,8, − 8} D. {0,8} 20. Findtherealsolutionsoftheequationbyfactoring. 3

2

x + 6x − 25x − 150 = 0 A. {5, − 6} B. {25, − 6} C. { − 5,5, − 6} D. { − 5,5,6}

21. Solvetheequation. |4x + 5| = 7

A. B. C.

− 1 2 2 5

1 2

,3

,−3 ,−

12 5

D. nosolution 22. Solvetheequation. |2x + 7| + 9 = 15

A.

1 13 , 2 2

B.

−

C.

−

1 7 1 2

,− ,−

13 7 13 2

D. nosolution 23. Listtheinterceptsofthegraph.

A. ( − 4,0),(0,4) B. ( − 4,0),(4,0)

y

10

C. (0, − 4),(4,0)

8

D. (0, − 4),(0,4)

6 4 2 10 8 6 4 2

2 4 6 8

10



x

2

4

6

8 10

24. Listtheinterceptsofthegraph.Tellwhetherthegraphis symmetricwithrespecttothe      x axis,y axis,origin,or noneofthese.

B. intercepts:( − 1,0),(0,0),(1,0) symmetricwithrespecttox axis,      y axis,andorigin

y

10 8

C. intercepts:( − 1,0),(0,0),(1,0) symmetricwithrespecttoy axis

6 4 2 10 8 6 4 2

2

x

2

4

6

8 10

4 6 8 10

25. Listtheinterceptsandtype(s)ofsymmetry,ifany. 2

y = x + 4 A. intercepts:(4,0),(0,2),(0, − 2) symmetricwithrespecttoxaxis B. intercepts:(0, − 4),(2,0),( − 2,0) symmetricwithrespecttoyaxis C. intercepts:( − 4,0),(0,2),(0, − 2) symmetricwithrespecttoxaxis D. intercepts:(0,4),(2,0),( − 2,0) symmetricwithrespecttoyaxis 26. Listtheinterceptsandtype(s)ofsymmetry,ifany. 2

A. intercepts:( − 1,0),(0,0),(1,0) symmetricwithrespecttox axis

2

16x + y = 16 A. intercepts:(4,0),( − 4,0),(0,1),(0, − 1) symmetricwithrespecttotheorigin B. intercepts:(4,0),( − 4,0),(0,1),(0, − 1) symmetricwithrespecttoxaxisandyaxis C. intercepts:(1,0),( − 1,0),(0,4),(0, − 4) symmetricwithrespecttoxaxisandyaxis D. intercepts:(1,0),( − 1,0),(0,4),(0, − 4) symmetricwithrespecttoxaxis,yaxis,andorigin

D. intercepts:( − 1,0),(0,0),(1,0) symmetricwithrespecttoorigin

27. Listtheinterceptsandtype(s)ofsymmetry,ifany.

y=

−x



2

x −8

A.

intercepts: 2 2 ,0 , − 2 2 ,0 ,(0,0) symmetricwithrespecttoorigin

B.

intercept:(0,0) symmetricwithrespecttoorigin

C.

intercept:(0,0) symmetricwithrespecttoyaxis

D.

intercept:(0,0) symmetricwithrespecttoxaxis

28. Findtheslopeofthelinecontainingthetwopoints. ( − 3,3);  (5,7) A. 2 B. C. D.

−

1 2

1 2 −2

29. GraphthelinecontainingthepointPandhavingslopem. P = ( − 3, − 4);  m = − 1 A.

B.

C.

y

10

y

10

10 10

y

10

x

10

D.

y

10

x

10

10 10

x

10

10 10

x

10

10 10

30. GraphthelinecontainingthepointPandhavingslopem. P = (3,0);  m = −

3 2

A.

B.

C.

y

D.

y

10

y

10 x

10

10

y

10

10

x

10

10

10

x

10

10

10

x

10

10

10 10

31. GraphthelinecontainingthepointPandhavingslopem. P = (7, − 8); slopeundefined A.

B.

C.

y

D.

y

10

y

10 x

10

10

y

10

10

x

10

10

10

x

10

10

10

x

10

10

32. Findanequationfortheline,intheindicatedform,withthegivenproperties. Containingthepoints (9, − 5)and ( − 3,6);generalform A.

− 14x + 9y = − 12

B. 14x − 9y = − 12 C.

− 11x + 12y = 39

D. 11x + 12y = 39 33. Findtheslopeinterceptformoftheequationofthelinewiththegivenproperties. xintercept = 3; y intercept = 5

A. y = − B. y =

5 3

C. y = − D. y = −

5 3

x+5

x+5 5 3 3 5

x+3 x+3

10 10

34. Findanequationforthelinewiththegivenproperties. Verticalline;containingthepoint( − 9, − 8) A. y = − 8 B. y = − 9 C. x = − 9 D. x = − 8 35. Findtheslopeinterceptformoftheequationofthelinewiththegivenproperties. Slope = 2; containingthepoint ( − 3,0) A. y = − 2x − 6 B. y = 2x + 6 C. y = − 2x + 6 D. y = 2x − 6 36. Findtheslopeandyinterceptoftheline. 9x + y = 7 7 1 A. slope = − ; y intercept = 9 9 B. slope = 9; y intercept = 7 9 1 C. slope = ; y intercept = 7 7 D. slope = − 9; y intercept = 7 37. Findanequationforthelinewiththegivenproperties. Paralleltotheline 8x + 7y = 86; containingthepoint (9, − 1) A. 9x + 7y = 86 B. 8x + 7y = 65 C. 8x − 7y = 65 D. 7x + 8y = − 1 38. Findanequationforthelinewiththegivenproperties. Perpendiculartotheline y =

A. y = 9x + − 13 B. y = − 9x − 13 C. y = − 9x + 13 D. y = −

1 9

x−

13 9

1 9

x + 3; containingthepoint(2, − 5)

39.

Findf(3)whenf(x) = A.

25

B.

13

C.

20

D.

21

2

x + 4x .

40. Findthedomainofthefunction. 2

f(x) = x + 7 A. {x|x ≠ − 7} B. {x|x > − 7} C. allrealnumbers D. {x|x ≥ − 7} 41. Findthedomainofthefunction. h(x) =

x−2 3

x − 25x A. {x|x ≠ 2} B. allrealnumbers C. {x|x ≠ 0} D. {x|x ≠ − 5,0,5} 42. Forthegivenfunctionsfandg,find f • gandstateitsdomain. f(x) = 3x − 3;  g(x) = 7x + 8 A. (f • g)(x) = 21x2 + 3x − 24; allrealnumbers B. (f • g)(x) = 21x2 − 13x − 24; {x|x ≠ − 24} C. (f • g)(x) = 21x2 − 24; {x|x ≠ − 24} D. (f • g)(x) = 10x2 + 3x + 5; allrealnumbers 43.

Find

A.

f g

2 ( − 5)whenf(x) = 2x − 7and g(x) = 4x + 14x + 5.

4 35

B. 0 C.

4 3

D.

−

17 35

44. Thegraphofafunctionisgiven.Decidewhetheritiseven, odd,orneither.

A. even B. odd

y

C. neither

12 10 8 6 4 2 1210 8 6 4 22

x

2 4 6 8 10 12

4 6 8 10 12

45. Determinealgebraicallywhetherthefunctioniseven,odd,orneither. 3

f(x) = 4x + 9 A. even B. odd C. neither 46. Determinealgebraicallywhetherthefunctioniseven,odd,orneither. f(x) =

1 x

2

A. even B. odd C. neither 47. Thegraphofafunctionisgiven.Determinewhetherthe functionisincreasing,decreasing,orconstantonthegiven interval.

A. decreasing B. constant C. increasing

(0,3) y

10 8 6 4 2 10 8 6 4 2

2 4 6 8

10

x

2

4

6

8 10

48. Thegraphofafunctionisgiven.Determinewhetherthe functionisincreasing,decreasing,orconstantonthegiven interval. (2,

A. constant B. decreasing C. increasing

) y

10 8 6 4 2 10 8 6 4 2

x

2

2

4

6

8 10

4 6 8 10

49. Usethegraphofthefunctionftoanswerthequestion.

A. fhasalocalmaximumatx = 0; the localmaximumis 1

Findthenumbers,ifany,atwhichfhasalocalmaximum. Whatarethelocalmaxima?

B. fhasnolocalmaximum C. fhasalocalmaximumat − ;thelocal maximumis 1

y

3

D. fhasalocalmaximumat x = − and ;thelocalmaximumis − 1

x

3 −

3

− −

2

2

2

2

3

50. Graphthefunction. x + 4 ifx < 1

f(x) =



− 5 ifx ≥ 1

A.

B.

C.

y

y

12

y

12

12 12

y

7

x

12

D. 7

x

12

12 12

x

12

12 7

x

7

7 7

51. Graphthefunction.

f(x) =

− x + 3 ifx < 2



2x − 3 ifx ≥ 2 A.

B.

C.

y

D.

y

6

y

6 x

6

6

6

6 6

x

6

6 6

52. Writetheequationofafunctionthathasthegivencharacteristics. 2

Thegraphof y = x ,shifted 9units upward

x

2

9

B. y = 9x 2 C. y = x 2 + 9 D. y = x 2 − 9 53. Writetheequationofafunctionthathasthegivencharacteristics. Thegraphof y = A. y =

x−4

B. y =

x +4

C. y =

x+4

D. y =

x −4

x, shifted 4unitstotheright

54. Writetheequationofafunctionthathasthegivencharacteristics. Thegraphof y = A. y =

x +7

B. y =

x −7

C. y =

x+7

D. y =

x−7

6

x

6

A. y =

y

6

x, shifted 7unitstotheleft

x

6

6 6

55. Writetheequationthatresultsinthedesiredtransformation. 2

Thegraphof y = x ,verticallystretchedbyafactorof 3 A. y = 3x 2 B. y = (x − 3)2 C. y = − 3x2 D. y = 3(x − 3)x 2 56. Matchthecorrectfunctiontothegraph.

A. y = − 2x2 + 1

y

B. y = − 2x2 − 1

6

C. y = 1 − x 2

4

D. y = − 2x2 2 x

6

4

2

2

4

6

2 4 6

57. Findthefunctionthatisfinallygraphedafterthefollowingtransformationsareappliedtothegraphof y = x . Thegraphis shiftedup 4 units,reflectedaboutthex axis,andfinallyshiftedleft 7 units. A. y =  − x − 7 + 4 B. y =  − x − 7 − 4 C. y =  − x + 7 + 4 D. y =  − x + 7 − 4 58. Graphthefunctionbystartingwiththegraphofthebasicfunctionandthenusingthetechniquesofshifting,compressing, stretching,and/orreflecting. f(x) = − x

2

A.

B.

C.

y

y

6

y

6

6 6

y

6

x

6

D. 6

x

6

6 6

x

6

6 6

x

6

6 6

59. Findthevertexandaxisofsymmetryofthegraphofthefunction. 2

f(x) = x + 10x A. ( − 5, − 25);  x = − 5 B. (25, − 5);  x = 25 C. ( − 25,5);  x = − 25 D. (5, − 25);  x = 5 60. Findthevertexandaxisofsymmetryofthegraphofthefunction. 2

f(x) = − x + 4x A. (2,4); x = 2 B. ( − 2, − 4);  x = − 2 C. (4, − 2);  x = 4 D. ( − 4,2);  x = − 4 61. Graphthefunctionusingitsvertex,axisofsymmetry,andintercepts. 2

f(x) = − x + 6x − 8 A.

B.

vertex(3,1) intercepts(4, 0), (2,0),(0, − 8)

C.

vertex( − 3, − 1) intercepts( − 4, 0), ( − 2,0),(0,8)

y

y

12

12

vertex( − 3, 1) intercepts( − 4, 0), ( − 2,0),(0, − 8)

y

12

y

12

x

12

D.

vertex(3, − 1) intercepts(4, 0), (2,0),(0,8)

12

x

12

12

12 12

62. Determinethedomainandtherangeofthefunction. 2

f(x) = − x + 10x A. domain:{x|x ≤ 5} range:{y|y ≤ 25} B. domain:{x|x ≤ − 5} range:{y|y ≤ 25} C. domain:allrealnumbers range:{y|y ≤ 25} D. domain:allrealnumbers range:{y|y ≤ − 25}

x

12

12 12

x

12

12 12

63. Determinewherethefunctionisincreasingandwhereitisdecreasing. 2

f(x) = x − 2x − 8 A. increasingon( − , − 9 ) decreasingon( − 9, ) B. increasingon( − ,1 ) decreasingon(1, ) C. increasingon( − 9, ) decreasingon( − , − 9 ) D. increasingon(1, ) decreasingon( − ,1 ) 64. Forthegivenfunctionsfandg,findtherequestedcompositefunctionvalue. f(x) =

x + 4 ,g(x) = 2x; Find (f g)(3).

A. 2 7 B. 2 4 C.

10

D.

14

65. Forthegivenfunctionsfandg,findtherequestedcompositefunction. f(x) =

x−5 2

,g(x) = 2x + 5; Find(g f)(x).

A. 2x + 5 B. x −

5 2

C. x D. x + 10 66. Isthefunctiononetoone? {( − 8,8),( − 7,8),( − 6, − 4),( − 5, − 4)} Yes No

67. Usethehorizontallinetesttodeterminewhetherthe functionisonetoone.

Onetoone Not onetoone

y

20 16 12 8 4

x

5 4 3 2 1 4

1

2

3

4

5

8 12 16 20

68. Arethefunctionsinversesofeachother? f(x) = 4x − 4,g(x) =

1 4

x+1

Yes No 69. Thefunctionfisonetoone.Finditsinverse. 3

f(x) = (x + 2) − 8 A. f − 1 (x) = 3 x + 8 − 2 B. f − 1 (x) = 3 x−2 +8 C. f − 1 (x) = 3 x + 10 D. f − 1 (x) = 3 x + 6 70. Solvetheequation. 4

7 − 3x

=

1 1,024

A. { − 4} B. {256} C.

1 256

D. {4}



71. Changetheexponentialexpressiontoanequivalentexpressioninvolvingalogarithm. 8

4 3

= 16

A. log 48 = log 3 16

B.

log 4 8

4 3 = 8

4 C. log 168 = 3 D. log 816 =

4 3

72. Changethelogarithmicexpressiontoanequiv...