Chapter 13 Answers - Poudre School District 30, 2013... · Algebra 2Chapter 13 Answers 39 Chapter...
Transcript of Chapter 13 Answers - Poudre School District 30, 2013... · Algebra 2Chapter 13 Answers 39 Chapter...
Algebra 2 Chapter 13 Answers 39
Chapter 13 Answers
Practice 13-11. not periodic 2. periodic; 2 3. periodic; 4. any two
points on the graph whose distance between them is one period;
sample: (0, 2) and (3 , 2); 5. any two points on the graph
whose distance between them is one period; sample: (0, 0) and
(4 , 0); 4 6. any two points on the graph whose distance
between them is one period; sample: (0, 2) and (4, 2); 4 7. ; 1
8. 3; 2 9. 2; 3 10. 6; 2 11. 6; 12. 13. 4; 2
14. 5; 15. ; 2 16. 4; 17. 5; 18.
Practice 13-21. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
O x
y
�355°O
x
y
�145°
Ox
y
145°
Ox
y
�120°
Ox
y
120°
Ox
y
�180°
Ox
y
315°
Ox
y
�45°
Ox
y
�330°O
x
y
�150°
Ox
y
�190°O
x
y
�90°
Ox
y
�30°Ox
y
330°
Ox
y
270°
O
x
y
210°
Ox
y
135°
Ox
y
100°
Ox
y
60°
Ox
y
30°
212, 15
811221
212315
8
123; 13
4134
18
218
14
14
313
13
314
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1340
21. 260° 22. 300° 23. 135° 24. 215° 25. 12° 26. 345°27. 122° 28. 124° 29. 340° 30. 61° 31. 49° 32. 322°33. 16° 34. 150° 35. 27° 36. 30° 37. 300° 38. 80°39. 190° 40. 10° 41. 20° 42. 98° 43. 120° 44. 46°45. 240° 46. 100° 47. 138° 48. 30° 49. 233° 50. 17°
51. ; (0.71, 0.71)
52. ; (-0.71,-0.71)
53. ; (-0.71, 0.71)
54. ; (0.71,-0.71)
55. ; (0.87,-0.5) 56. ; (0.87, 0.5)
57. ; (-0.87, 0.5)
58. ; (-0.87,-0.5)
59. ; (0.5,-0.87) 60. ; (0.5, 0.87)
61. ; (-0.5,-0.87) 62. ; (-0.5, 0.87)
63. (0,-1); (0,-1) 64. (1, 0); (1, 0) 65. (1, 0); (1, 0)
66. (0, 1); (0, 1) 67. ; (-0.71, 0.71)
68. ; (-0.5, 0.87) 69. -60° 70. 120° 71. 315°
Practice 13-31. 2. 3. 4. 5. p 6. 7.
8. 9. 2p 10. 11. 12. 13. 14.
15. 16. 180° 17. 360° 18. 150° 19. 135° 20. 270°
21. 30° 22. 210° 23. 330° 24. 60° 25. 240° 26. 225°
27. 315° 28. 120° 29. 20° 30. 40° 31.
32. 33. 34.
35. 36. 37.
38.
39. 11.0 in. 40. 39.8 cm 41. 10.5 cm 42. 92.2 cm 43. 2.1 ft44. 15.7 m 45. about 17.8 in. 46. 1.2 m
Practice 13-4
1. 4; 2p; y = 4 sin u 2. 1.5; ; y = 1.5 sin 4u
3. 2; 3p; y = -2 sin u 4. 1; 6p; y = sin u
5. 2.5; p; y = -2.5 sin 2u 6. 4; p; y = -4 sin 2u
7. ; y = 2 sin 2u
8. ; y = 3 sin u
9. ; y = 2 sin 4u
10. ; y = 2 sin 8u
11. ; y = 1.5 sin 6u
12. ; y = 2.5 sin u
13.
O
2
�2
2p 3pp
u
y
O
2
�2
2p 3pp
u
y
O
2
6 3�2
p
u
y
p p8
O
2
8 4�2
3pp
u
y
p8
O
2
4 2�2
3pp
u
y
p4
O
2
�2
2p 3pp
u
y
O
2
2�2
p 3pp
u
y
2
13
23
p2
212; "3
2
"32 ; 21
22 12; 2"3
22 "32 ; 12
"22 2 "2
22 "22 ; 2 "2
212; "3
2
"32 ; 12
11p9
10p9
8p9
11p18
4p9
2p9
5p3
3p2
4p3
5p6
p6
p2
p4
a212, "3
2 ba 2 "2
2 , "22 b
a212, "3
2 ba 2 12, 2 "32 b
a12, "3
2 ba12, 2 "3
2 ba 2 "3
2 , 2 12ba 2
"32 , 12b
a"32 , 1
2ba"32 , 21
2ba"2
2 , 2 "22 b
a 2"2
2 , "22 b
a 2"2
2 , 2"2
2 ba"2
2 , "22 b
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Algebra 2 Chapter 13 Answers 41
Chapter 13 Answers (continued)
14.
15.
16.
17.
18.
19.
20.
21.
22. about -0.1 23. about 0.2 24. about 0.2 25. 0.3 26. about 0.1 27. about 0.2 28. -0.3 29. about -0.2
Practice 13-51.
2.
3.
4.
5.
6.
O
2
�2
62 4
y
u
O
4
�4
2p 3pp
u
y
O
2
�2
2p 3pp
u
y
O
4
�4
2p 3pp
u
y
O
2
�2
62 4u
y
O
2
�2
2p 3pp
u
y
O
4
�4
2p 3pp u
y
O
4
5�4
3pp
u
y
52p5
O
4
2�4
p 3pp
u
y
2
O
4
3�4
p2pp
u
y
3
O
2
�2
p
u
y
23pp2
O
4
�4
2p 3pp
u
y
O
2
�2
p
u
y
23pp2
O
2
2�2
p 3pp
u
y
2
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1342
7.
8.
9.
10.
11.
12.
13.
14.
15.
16. y = 6 cos t 17. y = -5 cos u
18. y = 4 cos 2u 19. y = 3 cos 4u 20. 2p; 1; p; 0, 2p; ,
21. p; 4; 0, p, 2p; ,
22. 2p; 5; p; 0, 2p; 23. 0.24, 1.85, 2.34, 3.95, 4.43, 6.04
24. 2.36 25. 1.00, 3.00, 5.00 26. 1.34 27. 0.84, 5.44 28. 0
29. 2.67, 5.33 30. 4.19 31. 3.14 32. y = 2p cos 2pu
33. y = cos 2u
Practice 13-6
1. p; 2. 2p; p 3. 4p; 2p 4.
5. 2; 1, 3, 5 6. 1; 7.
8. 9.
10.
11.
12.
O
4
2�4
p 3pp u
y
2
O
4
2�4
p 3pp
u
y
2
O
4
2�4
p 3pp
y
2
u
1; 12, 32, 52, 72, 92, 112p; p2 , 3p2
p2 ; p4 , 3p4 , 5p4 , 7p4
12, 32, 52, 72, 92, 11
2
p2 ; p4 , 3p4 , 5p4 , 7p4
p2 , 3p2
12
p2 , 3p2
3p2 ; p4 , 3p4 , 5p4 , 7p4
p2
3p2
p2
2p5
O
4
�4
62 4
y
u
O
4
�4
62 4
y
u
O
2
2�2
p 3pp
u
y
2
O
2
�2
62 4
y
u
O
4
�4
62 4
y
u
O
4
2�4
p 3pp
u
y
2
O
2
�2
2p 3pp
u
y
O
4
2�4
p 3pp
u
y
2
O
2
�2
2p 3pp
u
y
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Algebra 2 Chapter 13 Answers 43
Chapter 13 Answers (continued)
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
O
4
2�4
3 93
u
y
2
O
4
2�4
p 3pp
y
2u
O
4
8�4
1 u
y
41
83
O
4
6�4
p
y
3p
2p u
O
4
8�4
p
y
4p
83p u
O
4
4�4
1
y
21
43 u
O
4
1 2 3
�4
y
u
O
4
4�4
3pp
y
2p
4
u
O
4
6�4
p
u
y
3p
O
4
1 2 3
�4
u
y
O
4
4�4
3pp
y
4u
2p
O
4
2�4
p 3pp
u
y
2
O
4
4�4
3pp u
y
2p
4
O
4
2�4
p 3pp u
y
2
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1344
27.
28. 29. p 30. 2p 31. undefined 32. 1 33. -1
34. undefined
35. ; 200, undefined,-2200
36. ;-14.9,-31.1,-50.1
37. ;-50, undefined, 50
Practice 13-71.
2.
3.
4.
5.
6.
7.
8.
9.
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
4
2�4
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
4
2�4
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
Xmin=0Xmax=470Xscl=50
Ymin=–300Ymax=300Yscl=100
Xmin=0Xmax=470Xscl=50
Ymin=–300Ymax=300Yscl=100
Xmin=0Xmax=470Xscl=50
Ymin=–300Ymax=300Yscl=100
p4
O
4
8�4
p
u
y
4p
83p
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Algebra 2 Chapter 13 Answers 45
Chapter 13 Answers (continued)
10.
11.
12.
13.
14.
15.
16. y = sin x - 2 17. y = cos (x + p) 18. y = cos x +
19. y = sin (x - 3.2) 20. 3; 2p; none; 2 units up
21. 2; 2p; units left; none 22. 1; p; none; 1 unit up
23. 1; 2p; units right; none 24. ; 2p; none; 3 units down
25. 1; 4p; none; 2 units down
26.
27.
28.
29
30.
31.
32. -2; 2 units to the left 33. 1; 1 unit to the right 34. -1.5; 1.5 units to the left 35. 1; 1 unit to the right
36. units to the right 37. -p; p units to the left
Practice 13-81. 0.86 2. 2 3. -1.10 4. -1 5. undefined 6. -1.07 7. 0.58 8. 14.14 9. -1.00 10. undefined 11. -1.01
12. 1.41 13. ; 1.41 14. undefined 15.
16. 2 17. undefined 18. - ;-1.41 19. undefined 20. 1
21. undefined 22. ; 1.15 23. - ;-1.15 24. 2 2"33
2"33
"2
2"33 ; 1.15"2
p2, p2
O
4
2 4
�4
y
x
O
2
�2
42
y
x
O
2
�2
42
y
x
O
4
�4�2
2
42
y
x
O
2
�2
42
y
x
O
4
2 4
�4
y
x
12
p3
p2
p4
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
4
2�4
p 3pp
y
2x
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
4
2�4
p 3pp
y
2
x
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1346
25. 26. 27. 28. -
29.
30.
31.
32.
33.
34.
35.
36.
37.
38. 1.73 39. undefined 40. 0.36 41. -5.76 42. 1.56 43. 1.02 44. 2.75 45. -2 46a.
46b. about 14.14 ft 46c. 10 ft
Reteaching 13-11. 6; 2 2. not periodic 3. 3; 2
Reteaching 13-2
1. 2. 3.
4. 5. 6.
Reteaching 13-3
1. 2. 3.
4. 5. 6.
7. -270° 8. 300° 9. 15° 10. 288° 11. -210° 12. 810°
Reteaching 13-41.
O
2
�2
2p 3pp
y
u
16p9 < 5.597p
4 < 5.50211p18 < 21.92
p4 < 0.795p
6 < 2.62p9 < 0.35
a2"22 , 2"2
2 ba212, "3
2 ba"22 , 2"2
2 ba"3
2 , 12ba"32 , 12ba2
"32 , 21
2b
O
10
2�10
1 31
y
2
t
O
2
2�2
p 3pp
u
y
2
O
2
2�2
p 3pp
u
y
2
O
2
2�2
p 3pp
u
y
2
O
4
2�4
p 3pp
u
y
2
O
2
2�2
p 3pp
y
2
uu
O
2
2�2
p 3pp
y
2
u
O
2
2�2
p 3pp
y
2
u
O
2
2�2
p 3pp
y
2
u
O
2
2�2
p 3pp
y
2
u
32
107
52
32
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Algebra 2 Chapter 13 Answers 47
Chapter 13 Answers (continued)
2.
3.
4.
5.
6.
7.
8.
9.
Reteaching 13-5
1. ; p;
2. 3; 4p;
3. 1; ;
4. ; 2;
5. 2; 4p;
6. 2; ;
7. 2; 2p;
O
2
�2
4p2p
y
u
O
2
2�2
1 31
y
2
u
13
O
2
�2
4p2p
y
u
O
1
�1
42 6u
y14
O
2
�2
p
u
y23 p
O
4
�4
4p 6p2p
y
u
O
2
2�2
p 3pp
y
2u
12
O
1
�1
2p 3pp
y
u
O
2
�2
2p 3pp
y
u
O
2
�2
2p 3pp
y
u
O
2
�2
2p 3pp
y
u
O
2
�2
4p 6p2p
y
u
O
1
�2
2p 3pp
y
u
O
4
�4
2p 3pp
y
u
O
1
�2
2p 3pp
y
u
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1348
8. 1; 10p;
9. 2; p;
Reteaching 13-6
1.
2. 2p; p;
3. p; ;
4. ;
5. 2; 1, 3, 5;
6. ;
7.
8. 2; 1, 3, 5;
9. 4; 2, 6;
Reteaching 13-71.
O
2
2�2
p 3pp
y
2
x
O
2
�2
p
y
u
O
2
�2
p
y
u
O
2
�2
p
y
u
p3 ; p6 , p2 , 5p6 , 7p6 , 3p2 , 11p
6 ;
O
2
�2
p
y
u
p; p2 , 3p2
O
2
�2
p
y
u
O
2
�2
p
y
u
p2 ; p4 , 3p4 , 5p4 , 7p4
O
2
�2
p
y
u
p2, 3p2
O
2
�2
p
y
u
O
2
�2
p
u
y
p2 ; p4 , 3p4 , 5p4 , 7p4 ;
O
2
�2
4p2p
y
u
O
2
�2
4p 6p2p
y
u
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Algebra 2 Chapter 13 Answers 49
Chapter 13 Answers (continued)
2.
3.
4.
5.
6.
7.
8.
9.
Reteaching 13-81.
2.
3.
4.
5.
6.
O
2
2�2
p 3pp
u
y
2
O
2
2�2
p 3pp
u
y
2
O
2
2�2
p 3pp u
y
2
O
4
2�4
p 3pp
u
y
2
O
2
2�2
p 3pp
u
y
2
O
2
2�2
p 3pp
y
2
u
O
4
2�4
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2x
O
2
2�2
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
O
4
2�4
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2x
O
4
2�4
p 3pp
y
2
x
O
2
2�2
p 3pp
y
2
x
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1350
7.
8.
9.
Enrichment 13-11. 2 2. 9 3. 8 4. 4 5. 7 6. 1 7. 5 8. 6 9. 3
A R I S T O T L E
Enrichment 13-21. about 1.16 miles 2. 23.2 miles 3. 13.92 miles 4. 0.1125 radians or about 6.4° 5. 0.627 radians or about 35.9°
Enrichment 13-3
1. 2. A = s 3. A = 4. S = rA 5. p radians
6. 7. 8. S = 2pVr
9. radians/s
Enrichment 13-41. 0.4226 2. 0.5878 3. 0.3256 4. 0.1908 5. 0.08726. 0.9703 7. 0.6561 8. 0.6157 9. 0.3746DOG; LOG; LEG; BEG; BAG; RAG
Enrichment 13-51. 0.087156; 0.087156; 0.087156
2. ; 0.190807; 0.190809; 0.190809; 0.190809
3. ; 0.438212; 0.438372; 0.438371; 0.438371
4. ; 0.600888; 0.601824; 0.601815; 0.601815
5. Answers may vary. Sample: The results indicate that Sn(x)approximates sin x to a greater degree of accuracy as nincreases. For x small, S3(x) is a good approximation to sin x;indicating that sin x < x for x small.6. 0.996192; 0.996195; 0.996195
7. ; 0.981571; 0.981627; 0.981627; 0.981627
8. ; 0.897039; 0.898806; 0.898794; 0.898794
9. ; 0.791489; 0.798735; 0.798635; 0.798636
10. Answers may vary. Sample: The results indicate that Cn(x)approximates cos x to a greater degree of accuracy as nincreases. For x small, C2(x) is a good approximation to cos x;indicating that cos x < 1 for x small.
Enrichment 13-61. (-a, b) 2. (-a,-b)
3. odd; f(-x) = -f(x)
4. ; even; f(-x) = f(x)
5. symmetrical about the origin; odd 6. symmetrical aboutthe y-axis; even 7. symmetrical about the origin; odd
Enrichment 13-71. 14 2. 264 3. 139
4. 125 5. 20; 6. y = 125 cos 7. 10; 139
8. y = 125 cos (x - 10) + 139
Enrichment 13-81. 1 2. sin A = y; cos A = x 3. (cos A, sin A)
4.5. (cos A)2
+ (sin A)2= 1
6.
7. 8.
9.
10.
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cos A
cos A 5 4"1 2 sin2A
"(cos A 2 0)2 1 (sin A 2 0)2 5 1
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Algebra 2 Chapter 13 Answers 51
Chapter 13 Answers (continued)
12.
Chapter ProjectActivity 1: EstimatingLocation 1: 12 h 25 min, 2.1 ft; Location 2: 12 h 25 min, 2.85 ft
Activity 2: Modeling
Check students’ work.
Activity 3: ResearchingCheck students’ work.
✔ Checkpoint Quiz 1
1. 2; 2 2. 1; 5 3. 4p; 3 4. 5.
6. 7. 8. 150° 9. 135° 10. Check students’ work.
✔ Checkpoint Quiz 21.
2.
3.
4.
5.
6.
7.
8.
9.
10.
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1352
Chapter Test, Form A1. not periodic 2. periodic; 3. 37° 4. 356° 5. 10°
6. 7. 8. 9. 315°
10. 300° 11. 1080° 12. 1; 3; 2p 13. 8; 4;
14. Answers may vary. Sample:
15. 11.0 in. 16. 3; ;
17. 2; ;
18. 1, 3, 5 19. 2.62, 3.67 20. 0.67, 3.33, 4.67
21. 0.73, 1.27, 2.73, 3.27, 4.73, 5.27 22. y =
23. y = 3 cos 4 u
24.
25.
26.
27. y = cos (x + 4) 28. y = sin + 2
29. 30. -1 31. 32. undefined
33.
34.
35. A vertical shift does not affect the amplitude of a periodic function.
Chapter Test, Form B
1. periodic; ; 2 2. not periodic 3. 320° 4. 30°
5. 6. -2p; -6.28 7. 900° 8. 120° 9. ; 1.5; 4p
10. 2; 2; p
11. 12.6 cm 12. 1; ;
13. 5; ;
14. 2.09, 4.19 15. 1.05, 3.14, 5.24 16. y =
17. y = 2 sin 8u
18.
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Algebra 2 Chapter 13 Answers 53
Chapter 13 Answers (continued)
19.
20. y = sin (x - 4) 21. y = cos (x + 1) + 3
22. 23. 2 24. 25. undefined
26.
27.
28. A phase shift does not affect the period of a periodic function.
Alternative Assessment, Form CTASK 1 Scoring Guide:
a. � 0.93 mi to the right, and � 0.37 mi up
b. � 0.38 radians; The answers stay the same.
c. � 0.38 mi; It is easier to work in radians because, in radi-ans, the arc length of a circle with a radius of 1 is givenby the numerical value of the angle that created the arc.
d. Check students’ work.
3 Student correctly finds the directions to move in part a.Student correctly converts degrees to radians, and findsthat the results are the same as in part a. Student cor-rectly determines arc length. Student provides a reason-able example that could be modeled by this situation.
2 Student correctly finds the directions to move in part a.Student converts degrees to radians and finds that theresults are the same as in part a with only minor errors.Student correctly determines the arc length with onlyminor errors. Student provides an example that could bemodeled by this situation.
1 Student finds the directions to move incorrectly in part a.Student incorrectly converts degrees to radians and doesnot compare the results with those in part a. Student incor-rectly determines the arc length. Student does not providean example that could be modeled by this situation.
0 Response is missing or inappropriate.
TASK 2 Scoring Guide:
a. Yes; in general, one 365-day year
b. Periodic, since every 365 days Earth is at the same basicposition with respect to the sun.
c. The amplitude is one-half of the difference between thefarthest Earth is from the sun and the closest Earth isfrom the sun during its orbit around the sun.
d. The amplitude, phase shift, and vertical shift of f(t) doesnot affect the amount of time that elapses between themaximum and minimum distances the Earth is from the sun.
e. Answers may vary. Sample: f(t) = sin 2pt.f. ; 0.5 yr
3 Student correctly identifies the period of Earth’s orbit,and that Earth’s orbit is best modeled by a periodic func-tion. Student correctly describes the amplitude of Earth’sorbit. Student correctly determines the amplitude, phaseshift, and vertical shift of f(t) does not affect time elapsedbetween max and min distance Earth is from the sun.Student determines a sine function f(t) with no errors.Student uses a graphing calculator to correctly identifythat one-half of a year elapses between max and min distances Earth is from the Sun.
2 Student correctly identifies the period of Earth’s orbit,and that Earth’s orbit is best modeled by a periodic func-tion. Student describes the amplitude of Earth’s orbitwith only minor errors. Student correctly determines theamplitude, phase shift, and vertical shift of f(t) does notaffect time elapsed between max and min distance Earthis from Sun. Student determines a sine function f(t) withonly minor errors. Student correctly uses a graphing calculator, and identifies that one-half of a year elapsesbetween max and min distances Earth is from the Sunwith only minor errors.
1 Student identifies Earth’s orbit as a periodic function.Student incorrectly describes the amplitude of Earth’sorbit. Student incorrectly determines the affect of theamplitude, phase shift, and vertical shift of f(t) on thetime elapsed between max and min distances Earth isfrom the Sun. Student incorrectly determines a sinefunction f(t). Student does not identify a time period of one-half of a year elapsing between max and min distances Earth is from the Sun.
0 Response is missing or inappropriate.
Xmin=0Xmax=1Xscl=.25
Ymin=–3Ymax=3Yscl=1
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Chapter 13 Answers (continued)
Answers Algebra 2 Chapter 1354
TASK 3 Scoring Guide:
a. Answers may vary. Sample: y = 2 sin
b. Answers may vary. Sample: y = 3 cos 4x + 1
c. Answers may vary. Sample: y = tan
d. yes; Check students’ work.
e. yes; Check students’ work.
3 Student correctly writes three functions. Student gives anaccurate explanation of shifting tangent and secant func-tions.
2 Student writes two of the three functions correctly.Student gives a reasonable explanation on shifting tangent and secant functions.
1 Student writes one of the three functions correctly, orhas minor errors in all three functions. Student gives anunclear or inaccurate explanation on shifting tangentand secant functions.
0 Response is missing or inappropriate.
TASK 4 Scoring Guide:Check students’ work.
3 Student describes a correct process for locating theasymptotes of a tangent function. Student gives clearand accurate descriptions of the relationships betweenthe reciprocal functions.
2 Student has errors in the description of locating theasymptotes of the tangent function. Student gives accurate descriptions of the relationships between thereciprocal functions.
1 Student has errors in the description of locating theasymptotes of the tangent function. Student gives aninaccurate description of the relationships between thereciprocal functions.
0 Response is missing or inappropriate.
Cumulative Review1. D 2. H 3. A 4. F 5. C 6. J 7. A 8. G 9. B 10. F11. D 12. F 13a. i 13b. 14a. 14b.15. y = 3x - 35 16. undefined 17. < 1.4 cm
18. 19. Answers may vary. Sample:
20. Shift the graph of y = cos x to the right units and up 1 unit.
p2
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