Chapter 2 Answers

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Chapter 2 Answers

Practice 2-1

1. -8; 212; 17; 37 2. 123; 116; 0; 2113 3. 7.8; 3.3; -7.2; -19.2 4. not a function 5. not a function 6. function

7.

y

10

6

; domain: {1, 2, 3, 5};

range:

e

22,

3 4

,

3 12 ,

9

f

2

x

O 24

8.

y

; domain: {-3, 0, 1};

range: {-2, 4, 5} 6

2 2 O

x 2

9.

y

; domain: {-1, 2, 3};

range: {2}

2

2 O

x 2

2

10.

y

; domain: {0.5};

range: {-1, 0, 1, 3}

2

2 O

x 2

2

11. not a function 12. function 13. not a function

14.

; not a function

1

2

2

3

3

4

5

15. 1 0 1 2 3

; function 0 1 4 9

16. 1

17. 3

18.

2 7

19.

10 3

Practice 2-2

1.

2 5

2. 5

3.

3 2

4. 221

5.

3 2

6. 2

7.

1 3

8. 272

9. y 2 1 5 213 (x 2 0)

10.

y

2

2 3

5

221 ax

2

1 2

b

11. y 1 2 5 2(x 1 3)

12.

y

13.

y

x

4

O 24

2

2

x

4

O 24

6

14.

y

2 2 O

x 2

2

15. 4x + y = 10 16. 2x - 5y = -17 17. y = -4 18. 34; (0, -3); (4, 0) 19. 0; (0, -2); none

20. 45; (0, 7); a2345, 0b 21. undefined; none; (5, 0)

22. y = 2x + 5;

y

23.

y

5

5 3

x

2

43 ;

y

2

2

2 O

x 2

2 O

x 2

2

2

24. x = -3;

y

25. y = 1;

y

2

2

2 O

x 2

2 O

x 2

2

2

Practice 2-3

1. 232; 292

2. 6; 18

3.

196 ;

27 16

4.

yes;

4 9

5. yes; -1.2

6. yes; -4

7. no

8. yes; 3

9. no

10.

yes;

3 5

11. no

12. no

13. yes; 3; y = 3x

14.

yes;

12 ;

y

5

1 2

x

15. no

Algebra 2 Chapter 2

Answers

35

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Chapter 2 Answers (continued)

16. y 5 13x

17. y = -6x

18. y = -18x

19.

y

5

3 7

x

20. y 5 23x

21. y 5 2365x

22.

y

5

5 2

x

23. y = 55x

24.

10 3

25. 2136

26. 11

27.

5 34

28. y = 0.06x; 22 min

29. 46.08 in.

Practice 2-4

1. y = 0.6x - 2.1 2. y = -2.04x + 7.548

3. y = 1.2x + 200; $214.40 4. y = 58x; 464 words

5. y = 146x + 5000; 6460 subscribers

6. 10 y

;

9

8

7

6 5 4

3

2

1

x

O 1 2 3 4 5 6 7 8 9 10

yes; using (3, 3.1) and (7, 5.2): y = 0.525x + 1.525

7. 10 y

; no

9

8

7

6 5 4

3

2

1

x

O 1 2 3 4 5 6 7 8 9 10

8.

y

;

4

2

2 O 2

x 2

4

yes; using (-1, -1.8) and (1, 1.9): y = 1.85x + 0.05

9. y

; no

6

5

4

3 2

1

x

O

123

10a. y 20

18

16

14

12

10

8

x

O 8 10 12 14 16 18 20

10b. using (9.4, 11.2) and (15.1, 19.1): y = 1.39x - 1.83 10c. about 15.5% 10d. yes

Practice 2-5

1. E 2. C 3. A 4. F 5. B 6. D

7.

y

8.

y

4

4

2

x O 24

2 O2

x 4

9.

y

10.

4

2

x 4 2 O

y 4

2 x

4 2 O 2

11.

y

12. y

x

6

4 2 O 2

4

2

2

4

x

O 24 6

13.

y

4

2

14.

y

2

2 O

2x

x

2

O 24 4

36

Answers

Algebra 2 Chapter 2

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Chapter 2 Answers (continued)

15.

y

4

16.

y

x

4 2 O 2

2

2

x

2 O

2

4

17. y

18.

y

4

2 x

O 246

2

2 O 2

x 2

19.

y

20.

y

2

x

2

2 O

2

2

2 O

x 2

2

4

21.

y

O2 2

4

x 4

Practice 2-6

1. horizontal; y

4

2. horizontal; y

4

2 4 2 O x

2

x 4 2 O

3. vertical;

4. diagonal;

y

y

2 O 2

x 2

2 2 O

x 2

4

2

5. diagonal; y

4 2

O2

6. horizontal; y

4

x 4

2 O2

x 4

7. vertical;

8. horizontal;

y

y

4

4

2

x

2

2 O 2 2

O2

9. diagonal; y

4

2 2 O

x 2

x 4

10. y = x + 2? + 1 11. y = x - 4?

12. y = -x - 1? + 3

13.

y

5

2` x

2

1 2

`

2

3 2

14. y = x + 3? - 2

15.

y

5

2ux u

1

3 5

16. y = x + 2? + 1 17. y = x? - 3 18. y = x + 2

19. h = 0; k = 2 20. h = 1; k = -2 21. h = -2; k = 0

22.

y

23.

y

x

4

2 O 2

2

2

x

2 O 2

4

Algebra 2 Chapter 2

Answers

37

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Chapter 2 Answers (continued)

24.

y

25.

y

x

4

4 2 O

2

2

x

4

2 O 2

26.

y

4

27.

y

4

2 2

x

O

2 4x

4 2 O 2

Practice 2-7

1. y x - 2 2. x - 2y 4 3. y - 2x 4

4. y -2 5. x 2 6. -2x - 3y 6

7. 3x - y 3 8. y - 3x 3

9.

y

10.

y

2

2

2 O

x 2

2 O

x 2

2

2

11.

y

12.

y

2 2 O

x 2

2 2 O

x 2

2

2

13.

y

14.

y

2

2

x

x

2 O

2 O

2

2

15.

y

2

2 O 2

16.

y

x 2

2 O 2

x 2

17.

y

2

2 O 2

18.

x 2

y 2

2 O 2

x 2

19.

y

2

2 O 2

20.

x 2

y 2

2 O 2

x 2

21.

y

2

2 O 2

22.

x 2

y 2

2 O 2

x 2

23.

y

2

2 O 2

24.

x 2

y 2

2 O 2

x 2

25.

y

4

2

2 O

26.

y

2

x 2

2 O 2

x 2

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Answers

Algebra 2 Chapter 2

A2_3eCSF02_027-046 8/5/02 5:54 PM Page 39

Chapter 2 Answers (continued)

27.

y

28.

y

2 x

O2 2

2

2 O 2

x 2

29a. x + y 150, where x represents the number of tuna sandwiches and y represents the number of ham sandwiches 29b. 200 y

150

100

50

x O 50 100 150 200

29c. Yes; the sum of 90 and 80 is more than 150. 30a. 150x + 200y 1800, where x represents the number of $150 models and y represents the number of $200 models 30b. 16 y

12

8

4

x

O

4 8 12 16

30c. at least four $150 models

Reteaching 2-1

1.?4. Check students' work. 5. No; the x-value 1 is repeated

with different y-values; domain: {1}; range: {2, 3, 4, 5, 6}

6. Yes; no x-value is repeated; domain: {0, 1, -1, -2, 2};

range: {-1, 2, 5, 9}

7. Yes; no x-value is repeated; domain: {A, C, E, G}; range:

{B, D, F, H} 8. No; the x-value I is repeated with different

y-values; domain: {I, N}; range: {M, P, T} 9. Yes; no x-value is

repeated; domain: {0}; range: {0}

10.

No;

the

x-value

1 2

5

0.5

is repeated with range: {3, 4, 1}

different

y-values;

domain:

e

12 ,

2

f

;

Reteaching 2-2

1. y = 4x - 10 2. y = -2x + 15 3. y = 0

4. y = -x - 7 5. y = 3x + 2 6. y = -7

7. y = 8x - 40 8. y = -x + 7 9. y = 8

10. y = 4x - 3 11. y = 7x - 19 12. y = -x - 4

13. y = 2x + 3

14. y = -x - 2

15.

y

5

2 3

x

1

2

Reteaching 2-3

1. 12

2. 20

3.

7 3

4. -3

5. 4

6.

6 7

7. 261147 ft

Reteaching 2-4

1.

y

32

Percent of U.S. Population Enrolled in HMOs

28

24

20

16

12

8

4

x

0

'92 '94 '96 '98 '00

Year

2.

y

32

; using (0, 14.3) and (7, 30.1):

Percent of U.S. Population Enrolled in HMOs

28

y = 2.26x + 14.3

24

20

16

12

8

4

x

0

'92 '94 '96 '98 '00

Year

3. about 45.9%

Reteaching 2-5

1. (0, 0) 2. (-3, 0) 3. (4, 0) 4. a213, 0b 5. (6, 0) 6. (-8, 0)

7. a 21, 0b;

y

4

2 O

x 2

8. a 31, 0b;

y 6

4

2 2 O

x 2

Algebra 2 Chapter 2

Answers

39

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Chapter 2 Answers (continued)

9. (-2, 0);

y

6

4

2

x 4 2 O

10. (-1, 0);

y

6

4

11. (2, 0);

2

2 O y

6

x 2

4

2 2 O

x 24

12. a34, 0b;

y

6

4

2

2 O

2x

13. (0, 0);

y

6

4

2

2 O 14. (-2, 0);

x 2

y 4

2 x

4 2 O 2

15. (-3, 0);

y

4

2 x

4 2 O 2

Reteaching 2-6

1. right;

y

2

2 O 2

x 2

2. up;

y

2

2 O 2

x 2

3. down;

y

2

2 O 2

2x

4. left;

y

2

x 4 2 O

2

5. right; down;

y x

2 O 2

2

4

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Answers

Algebra 2 Chapter 2

A2_3eCSF02_027-046 8/5/02 5:54 PM Page 41

Chapter 2 Answers (continued)

6. left; up;

y

4

2

x 6 4 2 O

Reteaching 2-7

1.

y

2.

2

2 O 2

x 2

y 4 2

O2

x 4

3.

y

4

2

2 O 2 2

4.

x 4

y

2

2 O 2

x 2

5.

y

4

6.

y

4

2

x O 24

2

x 4 2 O 2

7.

y

8.

4

2 x

4 2 O 2

2

y 2

2 O x 2

9.

y

10.

y

4 2 2 O

2x

2 x

O 24

2

11.

y

12.

y

2

2

2 O

x 2

2 O

x 2

2

2

13.

y

14.

y

2

2 O 2

x 2

2

2 O 2

x 2

15.

y

2

2 O 2

x 2

Enrichment 2-1

1. The line y = x must contain the graph of the relation. 2. The relation is empty. 3. equivalence relation 4. reflexive, transitive 5. asymmetric, transitive 6. none 7. symmetric, transitive 8. transitive 9. symmetric 10. symmetric 11. reflexive 12. symmetric 13. symmetric, transitive 14. symmetric 15. asymmetric

Enrichment 2-2

1. y = -3x + 8; (3, -1) 2. (5, -7) 3. (3, -1); (5, -7)

4.

t

=

x

2 2

1

5. y = -3x + 8 6. linear; -3 7. (0, 8)

8. y = -4x - 25 9. y = -x + 8

Enrichment 2-3

1. Jones: 3.5%; Ortiz: 9% 2a. direct variation; 4

2b. direct variation; 243 2c. not direct variation

2d.

direct

variation;

1 30

3a. not direct variation

3b. direct variation; -3 3c. not direct variation

3d. not direct variation 4a. direct variation; 2

4b.

direct

variation;

5 4

4c. not direct variation

4d.

direct

variation;

11 3

5. y is multiplied by 8.

6. the value of the constant of variation 7. 50 volts

Algebra 2 Chapter 2

Answers

41

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Chapter 2 Answers (continued)

Enrichment 2-4

1. (0, 350), (3, 75) 2. 22735 3. y 5 22735x 1 350 4. 258?F; 167?F; -17?F 5. no 6. 275?F 7. 233.75?F 8. 116.25?F; very close

Enrichment 2-5

1. x

0 -1 -2 -3 -2 -1 0

y -3 -2 -1 0 1 2 3

y

2

2 O 2

x 2

2. No; the x-value 0 is paired with two y-values: -3 and 3.

3. x + y = 2 or x + y = -2

4.

y

2 2 O

x 2

2

5. No; every vertical line intersects the graph in two points.

6.

y

; function

x

2 O 2

2

4

7.

y

2

2 O 2

; not a function x

8.

y

; function

2

2 O

x 2

2

9.

y

; not a function

2

x 4 2 O

2

10.

y

; function

4

2 2 O

x 2

11.

y

4

; not a function

2 x

O 24

2

Enrichment 2-6

1. x

3210123

y -3 -2 -1 0 1 2 3

y

2

2 O 2

x 2

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42

Answers

Algebra 2 Chapter 2

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