Precalculus: An Investigation of Functions by David Lippman and Melonie Rasmussen - HTML preview

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