11. More than $42,857.14 worth of jewelry
13. 20.012 square units
15. 6 square units
2
17.
b
A = −
2 m
19a. Hawaii
b. $80,640
c. During the year 1933
21. 26.225 miles
529
Section 2.4
1.
http://www.mathcracker.com/scatter_plot.php
3. y =1.971 x − 3.519, r = 0.967
5. y = 0.901
−
x + 26.04, r = 0.968
−
7. 17.483 ≈17 situps
9. D
11. A
13. Yes, trend appears linear because r =0.994 and will exceed 35% near the end of the
year 2019.
Section 2.5
1.
1
y = x + 2 +1
3. y = 3
− x − 3 + 3
2
5.
7.
9.
11.
9
13
x = − or x =
13.
1
15
x = or x =
5
5
2
2
15.
5
1
x = − or x = −
3
3
Horizontal Intercepts
Vertical Intercept
17.
(-6, 0 ) and (4, 0)
(0, -8)
19.
none
(0, -7)
21. 11
− < x <1 or (−
)
1
,
11
23. x ≥ 5 , x ≤ 1
− or (−∞,− ]
1 ∪ ,
5
[ ∞)
25. 13
5
−
< x < − or 13 5
(− ,− )
3
3
3
3
530
Chapter 3
Section 3.1
1. As x → ∞, f ( x) → ∞
As x → −∞, f ( x) → ∞
3. As x → ∞, f ( x) → ∞
As x → −∞, f ( x) → −∞
5. As x → ∞, f ( x) → −∞ As x → −∞, f ( x) → −∞
7. As x → ∞, f ( x) → −∞ As x → −∞, f ( x) → ∞
9. 7th Degree, Leading coefficient 4
11. 2nd Degree, Leading coefficient -1
13. 4th Degree, Leading coefficient -2
15. 3rd Degree, Leading coefficient 6
17. As x → ∞, f ( x) → −∞ As x → −∞, f ( x) → −∞
19. As x → ∞, f ( x) → ∞ As x → −∞, f ( x) → ∞
21. intercepts: 5, turning points: 4
23. 3
25. 5
27. 3
29. 5
31. Horizontal Intercepts (1,0), (-2, 0), (3, 0) Vertical Intercept (0, 12)
33. Horizontal Intercepts (1/3, 0) (-1/2, 0) Vertical Intercept (0, 2)
Section 3.2
1. f ( x) = ( x − 2)2 − 3
3. f ( x) = − (
2 x − 2)2 + 7
5. f ( x) 1
= ( x − 3)2 −1
2
Vertex
Vertical Intercept Horizontal Intercepts
7. ( 2.5
− , 0.5
−
)
(0,12)
(-2, 0) (-3, 0)
9. (2.5, 8.5
−
)
(0,4)
(0.438, 0) (4.562,0)
11. (0.75,1.25)
(0,-1)
(0.191, 0) (1.309, 0)
13. f ( x) = ( x − )2
6 − 4
15. f ( x) = (
2 x + 2)2 −18
17. b = 32 and c = -39
19. f ( x)
2
= − ( x + )
3 ( x − )
1
21. f ( x) 3
= ( x − 2)( x − 5)
3
5
23. f ( x)
1
= − ( x − 4)2
25. f ( x)
1
= − ( x + 3)2 + 2
4
9
27a. 234m
b. 2909.561 ft
c. 47.735 seconds
29a. 3 ft
b. 111 ft
c. 72.497 ft
31. 24.91 in by 24.91 in
33. 125 ft by 1
83 ft
3
35. 24.6344 cm
37. $10.70
531
Section 3.3
C(t)
C,
t, intercepts
intercepts
1.
(0,48)
(4,0), (-1,0), (6,0)
3.
(0,0)
(0,0), (2,0), (-1,0)
5.
(0,0)
(0,0), (1,0), (3,0)
7. (-1.646, 0) (3.646, 0) (5,0)
9. As t → ∞, h
( t) → ∞
t
→ −∞, h
( t) → −∞
11. As t → ∞, p
( t) → −∞
t
→ −∞, p
( t) → −∞
13.
15.
17.
19. (3,∞)
21.(−∞, 2
− )∪(1,3)
23. [3.5,6]
25. (−∞, ]
1
(
4,∞
∪
)
27. [3,∞)
29. (−∞, 4
− ) ( 4,
− 2) (2,∞
∪
∪
)
31.
2
y = − ( x + 2)( x − )
1 ( x − 3)
33.
1
y = ( x − )
1 2 ( x − )
3 2 ( x + )
3
3
3
35. y = − ( x − )2 ( x − )3
15
1
3
37.
1
y = ( x + 2)( x − )
1 ( x − 3)
2
39. y = −( x + )
1 2 ( x − )
2
41.
1
y = −
( x +3)( x + 2)( x − 2)( x − 4)
24
43.
1
y =
( x + 4)( x + 2)( x − )2
3
45.
1
y =
( x + 2)2( x − )2
3
24
12
47.
1
y = ( x + 3)( x + 2)( x − )3
1
49.
1
y = − ( x + 3)( x + )
1 ( x − 2)2 ( x − 4)
6
16
51. Base 2.58, Height 3.336
532
Section 3.4
1. D
3. A
Vertical
Horizontal
Vertical y-
Horizontal x-
Asymptotes
Asymptote
Intercept
intercept
5.
x = 4
−
y = 2
(0,-3/4)
(3/2, 0)
7.
x = 2
y = 0
(0,1)
DNE
9.
1
y =
(0, 5/16)
(-1/3, 0), (5,0)
x
1
=
,
4
− 1
3
11.
x = 1
− , hole at
y =1
(0,3)
(-3, 0)
x =1
13.
x = 4
none
(0, ¼)
(-1, 0), (1/2, 0)
y=2x (oblique)
15.
x = ,
0 4
y = 0
DNE
(-2, 0), (2/3, 0)
17.
x = ,
2
− 4
y =1
(0, -15/16)
(1, 0), (-3, 0), (5, 0)
5.
7.
9.
11.
13.
15.
533
17.
50( x − 2)( x + )
1
7( x − 4)( x + 6)
19. y = (
21. y =
x + 5)( x − 5)
( x + 4)( x +5)
( x − )2
1
2
4( x − 3)
23. y =
25. y =
2( x + )
1
( x +3)( x − 4)
27( x − 2)
1( x + 3)( x − 2)
27. y =
29. y =
( x +3)( x −3)2
3( x − )
1
− (
6 x − )2
2( x)( x − 3)
31.
1
y = (
33. y = −
x + 3)( x − 2)2
( x +3)( x − 4)
2( x − )3
1
( x − 4)( x − 2)
35. y =
37. y =
( x + )1( x − 2)2
( x − 4)( x + )1
39. a. C( n =
4
)
b. C )
10
(
≈
%
33
.
13
c. 80 mL d. as n → ∞, C → 0
20 + n
Section 3.5
1. Domain (4,∞) Inverse 1
f − ( x) = x + 4
3. Domain (−∞,0) Inverse 1
f − ( x) = − 12 − x
−
5. Domain (−∞,∞) Inverse 1
f − ( x)
x 1
= 3
3
−
3
−
x 9
−
7. f ( x) (
)2
1
=
+1
9. 1
f − ( x)
x 9
=
4
2
−
−
11. 1− ( ) 2 8 x
f
x =
13. 1− ( ) 3 7 x
f
x =
x
x −1
−
−
15. f 1( ) 5 x
x
4
=
17. 65.574 mph
3 + 4 x
19. 34.073 mph
21. 14.142 feet
534
Chapter 4
Section 4.1
1. Linear
3. Exponential
5. Neither
7. ( ) 11,000(1.085) t
P t =
9. 47622 Fox
11. $17561.70
13.
6(5) x
y =
15.
2000( )
0.1 x
y =
3
x
−
17.
3(2) x
y =
19.
5
5
1 1
y
=
x
1
x
= 2.93(0.699) 21. y = (2)
6 6
8
23.34.32 mg
25. 1.39%; $155,368.09
27. $4,813.55
29. Annual ≈ $7353.84 Quarterly ≈ $7,469.63
Monthly ≈ $7,496.71
Continuously ≈ $7,510.44
31. 3.03%
33. 7.4 years
35a. ( ) (1.113)(1.046) t
w t =
b. $1.11
c. Below what the model predicts ≈ $5.70
Section 4.2
1. B
3. A
5. E
7. D
9. C
11.
13.
15.
17.
4 x
y = + 4
19.
2
4 x
y
+
=
21.
4 x
y = −
23. As x → ∞ f ( x) → −∞ . As x → −∞ f ( x) → 1
−
25. As x → ∞ f ( x) → 2
− As x → −∞ f ( x) → ∞
27. As x → ∞ f ( x) → 2 As x → −∞ f ( x) → ∞
29. y = 2 x+2
−
+1 = 4
− ( )
2 x +1
31. = − (
2 )
2 − x
y
+ 3
x
33. = − (
2 3) x
y
+ 7
35.
1
y = 2
− 4
2
Section 4.3
1. 4 m = q
3. c
a = b
5.10 t = v
7. n
e = w