Answers

Chapter P

Section P.1

1. Independent, dependent

2. True

3. False

4. False

5. False

6. Vertical

7. 5,−3

8. −2

9. (a)

10. (a), (b)

11. False

12. 8

13. (a) −4

(b) 3x2−2x−4

(c) −3x2−2x+4

(d) 3x2+8x+1

(e) 3x2+6xh+3h2+2x+2h−4

15. (a) 4

(b) |x|+4

(c) −|x|−4

(d) |x + 1| + 4

(e) |x + h| + 4

17. (,)

19. (−,−3] [3,)

21. {x|x ≠ −2, 0, 2}

23. −3

25.

27. 2x + h + 2

29. It is not a function.

31. (a) Domain: [−π, π], range: [−1, 1]

(b) Intercepts: , (0,1)

(c) Symmetric with respect to the y-axis, but not with respect to the x-axis or the origin.

33. (a) f (−1) = 2, f (0) = 3, f (1) = 5, f (8) = −6

(b)

(c) Domain: [−2,), range: (−, 4) {5}, intercepts: (0, 3), (2, 0)

35. (a) f (−1) = 0, f (0) = 0, f (1) = 1, f (8) = 64

(b)

(c) Domain: (−,), range: (−,), intercepts: (−1, 0), (0, 0)

37. f (0) = 3, f (−6) = −3

39. Negative

41. (−3, 6) (10, 11]

43. [−3, 3]

45. 3

47. Once

49. −5, 8

51. (4, 8)

53. (0, 8)

55. {x|x ≠ 6}

57. −3, (4,−3)

59. −2

61. Odd; symmetric with respect to the origin, but not with respect to the x-axis or the y-axis.

63. Neither; not symmetric to the x-axis, y-axis, or the origin.

65. (a) −4

(b) −8

(c) −10

(d) −2(x + 1)

67. f (x) =

69. f (x) =

71. f (x) =

73. (a) $250.60

(b) $2655.40

(c) Answers will vary.

Section P.2

1. (a)

2. True

3. True

4. False

5. False

6. Zero

7. (b)

8. True

9. True

10. False

11. D

13. F

15. C

17. G

19. (a) 2

(b) 3

(c) −4

21. (a) 7 with multiplicity 1; −4 with multiplicity 3

(b) x-intercepts: 7, −4, y-intercept: −1344

(c) Crosses at 7 and at −4

23. (c), (e), (f)

25. Domain: {x|x ≠ −3}, intercept: (0, 0)

27. Domain: (−,), intercepts: (0, 0),

29. (a) A(x) = 16xx3

(b) [0, 4]

31. (a) The pattern in the scatter plot suggests a quadratic relationship.


(b) 283.8 feet

(c) 15.63 feet

Section P.3

1. {x|0 ≤ x ≤ 5}

2. False

3. True

4. False

5. True

6. False

7. True

8. Horizontal, right

9. y

10. −5, −2, 2

11. (a) (f + g)(x) = 5x + 1, domain: (−,)

(b) (fg)(x) = x + 7, domain: (−,)

(c) (fg)(x) = 6x2x − 12, domain: (−,)

(d)

13. (a) (f + g)(x) = , domain: {x| − 1 ≤ x < 0} {x|x = 0}

(b) , domain: {x| − 1 ≤ x < 0} {x|x = 0}

(c) (fg)(x) = , domain: {x| − 1 ≤ x < 0} {x|x = 0}

(d) , domain: {x|x ≥ −1, x = 0}

15. (a) (fg)(4) = 98

(b) (gf)(2) = 49

(c) (ff)(1) = 4

(d) (gg)(0) = 4

17. (a) (fg)(1) = −1

(b) (fg)(−1) = −1

(c) (gf)(−1) = 8

(d) (gf)(1) = 8

(e) (gg)(−2) = 8

(f) (ff)(−1) = −7

19. (a) (gf)(−1) = 4

(b) (gf)(6) = 2

(c) (fg)(6) = 1

(d) (fg)(4) = −2

21. (a) (fg)(x) = 24x + 1, domain: (−,)

(b) (gf)(x) = 24x + 8, domain: (−,)

(c) (ff)(x) = 9x + 4, domain: (−,)

(d) (gg)(x) = 64x, domain: (−,)

23. (a) (fg)(x) = x, domain: {x|x ≥ 1}

(b) (gf)(x) = |x|, domain: (−,)

(c) (ff)(x) = x4 + 2x2 + 2, domain: (−,)

(d) (gg)(x) = , domain: {x|x ≥ 2}

25. (a) (fg)(x) = , domain: {x|x ≠ 0, x ≠ 2}

(b) (gf)(x) = , domain: {x|x ≠ 0, x ≠ 1}

(c) (ff)(x) = x, domain: {x|x ≠ 1}

(d) (gg)(x) = x, domain: {x|x ≠ 0}

27. f (x) = x4, g(x) = 2x + 3

29. f (x) = , g(x) = x2 + 1

31. f (x) = |x|, g(x) = 2x + 1

33.

35.

37.

39.

41.

43.

45.

47. (a)

(b)

(c)

(d)

(e)

(f)

(g)

49. (a)

(b)

(c) Answers will vary.

(d)

(e) Answers will vary.

Section P.4

1. False

2. [4,)

3. False

4. True

5. False

6. False

7. Answers will vary.

8. Answers will vary.

9. One-to-one

11. Not one-to-one

13. One-to-one

15. See Student Solutions Manual.

17. See Student Solutions Manual.

19. (a) One-to-one

(b) {(5,−3), (9,−2), (2,−1), (11, 0), (−5, 1)},

(c) Domain of f: {−3,−2,−1, 0, 1}, range of f: {−5, 2, 5, 9, 11}, domain of f−1: {−5, 2, 5, 9, 11}, range of f−1: {−3,−2,−1, 0, 1}

21. (a) Not one-to-one

(b) Does not apply

(c) Domain of f: {−10,−3,−2, 1, 2}, range of f: {0, 1, 2, 9}

23.

25.

27.

29. (a) f−1 (x) =

(b) Both the domain and range of f are (−,). Both the domain and range of f−1 are (−,).

31. (a) f−1 (x) = x3 − 10

(b) Both the domain and range of f are (−,). Both the domain and range of f−1 are (−,).

33. (a) f−1 (x) = 2 +

(b) Domain of f: {x|x = 2}, range of f: {y|y = 0}, domain of f−1: {x|x = 0}, range of f−1: {y|y = 2}

35. (a) f−1 (x) =

(b) Domain of f: {x|x = −2}, range of f: {y|y = 2}, domain of f−1: {x|x = 2}, range of f−1: {y|y = −2}

37. (a) f−1 (x) =

(b) Domain of f: {x|x ≥ 0}, range of f: {y|y ≥ 4}, domain of f−1: {x|x ≥ 4}, range of f−1: {y|y ≥ 0}

Section P.5

1. , (0, 1), (1, a)

2. False

3. 4

4. 3

5. False

6. False

7. 1

8. {x|x = 0}

9. , (1, 0), (a, 1)

10. (a)

11. False

12. True

13. True

14. 1

15. Answers will vary.

16. 0

17. (a) g(−1) = ,

(b) x = 3, (3, 66)

19. (a)

21. (c)

23. (b)

25. Domain: (−,), range: (0,)

27. Domain: (−,), range: (0,)

29. Domain: (−,), range: (0,)

31. {x|x ≠ 0}

33. {x|x = 1}

35. (b)

37. (f)

39. (c)

41. (a) {x|x = −4}

(b and f)

(c)
(−,)

(d) f −1(x) = ex − 4

(e) (−,)

43. (a) (−,)

(b and f)

(c) {y|y = 2}

(d) f −1(x) =

(e) {y|y = 2}

45. It shifts the x-intercept c units to the left.

47. x = 0, x = 2

49. x =

51. x =

53. x =

55. x =

57. x =

59. x =

61. x = 3

63. x ≈ 2.787

65. x ≈ 1.315

67. (a)

(b)

(c)

Section P.6

1. 2π, π

2. All real numbers except odd multiples of

3. {y| − 1 ≤ y ≤ 1}

4. The period of tan x is π.

5. False

6. 3,

7. True

8. False

9. True

10. Origin

11. y-axis

12. Answers will vary.

13. −1

15.

17. 0

19. −1

21. (f)

23. (a)

25. (d)

27.

29.

31.

33. , 2

35. 3, 2π

37. f (x) = 2 sin(2x)

39. f (x) = cos(2x)

41. f (x) = −sin

43. f (x) = 1 – cos

45. f (x) = cot x

47. f (x) = tan

Section P.7

1. sin y

2. False

3. False

4. True

5. False

6. True

7. True

8. True

9.

11.

13.

15.

17.

19.

21.

23.

25. See Student Solutions Manual.

27.

29.

31.

33.

35.

37.

39.

41.

43.

45. {1.373, 4.515}

47. {3.871, 5.553}

49. (a and c)

(b)

(c) See (a).

(d)