Solution Manual For Calculus 10th Edition by Ron Larson, Bruce Edwards |Updated Version A+

NOT FOR SALE
CHAPTER P
Preparation for Calculus

Section P.1 Graphs and Models.................................................................................2

Section P.2 Linear Models and Rates of Change....................................................11

Section P.3 Functions and Their Graphs.................................................................22

Section P.4 Fitting Models to Data..........................................................................34

Review Exercises ..........................................................................................................37

Problem Solving ...........................................................................................................43




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, NOT FOR SALE
C H A P T E R P
Preparation for Calculus
Section P.1 Graphs and Models
1. y  32 x  3 7. y 4  x2
x-intercept: (2, 0)
x 3 2 0 2 3
y-intercept: (0, 3)
y 5 0 4 0 5
Matches graph (b).
y

2. y 9  x2 6

x-intercepts: 3, 0 , 3, 0 (0, 4)

2
y-intercept: (0, 3) (− 2, 0) (2, 0)
x
−6 −4 4 6
Matches graph (d). −2

(− 3, − 5) −4 (3, − 5)
3. y 3  x2 −6


x-intercepts: 3, 0 ,  3, 0
2
8. y x3
y-intercept: (0, 3)
Matches graph (a).
x 0 1 2 3 4 5 6
4. y x  x
3
y 9 4 1 0 1 4 9
x-intercepts: 0, 0 , 1, 0 , 1, 0 y


y-intercept: (0, 0) 10
(0, 9) (6, 9)
8
Matches graph (c).
6

4 (1, 4) (5, 4)
5. y 1x
2
 2 (2, 1)
2
(4, 1)
x
x 4 2 0 2 4 −6 −4 −2
−2
2 4 6
(3, 0)

y 0 1 2 3 4
9. y x  2
y


6 x 5 4 3 2 1 0 1
(4, 4)
4 (2, 3) y 3 2 1 0 1 2 3
(0, 2)
(−2, 1) y
x
−4 −2 2 4 6
(−4, 0) −2
4
(− 5, 3)
(1, 3)
6. y 5  2x (− 4, 2) 2 (0, 2)
(− 3, 1) (− 1, 1)
x
x 1 0 1 2 5
2
3 4 −6 −4 (− 2, 0) 2

−2
y 7 5 3 1 0 1 3
y

8
(− 1, 7)
(0, 5)
4
(1, 3)
2
(2, 1)
x
−6 − 4 −2 (3, −1)
( (
−2




INSTRUCTOR
ST USE ONLY
5,0
2 ( , −3)
(4, 3))
−
−44




2 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© Cengage Learning. All Rights Reserved.

, NOT FOR SALE Section P.1 Graph
Graphs and Models 3


10. y x 1 1
14. y
x 2
x 3 2 1 0 1 2 3
x 6 4 3 2 1 0 2
y 2 1 0 1 0 1 2
y  14  12 1 Undef. 1 1
2
1
4
y

y
4

3 5
4
(−3, 2) 2 (3, 2) 3 (0, 12 )
2
(− 2, 1) (2, 1) (− 1, 1)
(2, 14 )
x x
−3 −2 1 2 3 −1 1 2 3
(− 1, 0) −1 (1, 0) (− 6, − 14 ) −2
−2 (0, − 1) (− 4, − 12 ) −3
−4
(−3, − 1)
−5


11. y x 6
15. y 5 x
x 0 1 4 9 16
5

y 6 5 4 3 2 (−4.00, 3)
(2, 1.73)
y
−6 6

2

x −3
−4 4 8 12 16
−2 (9, − 3)
(16, −2) (a) 2, y 2, 1.73 y 52 3 | 1.73
−4 (4, −4)
(1, − 5)
−6
(0, −6)
(b) x, 3 4, 3 3 5  4
−8



16. y x5  5 x
12. y x  2
6
(−0.5, 2.47)
x 2 1 0 2 7 14
−9 9
y 0 1 2 2 3 4
(1, −4)
y
−6
5

4
(a) 0.5, y 0.5, 2.47
(14, 4)
3
(− 1, 1)
(7, 3) (b) x,  4 1.65,  4 and x,  4 1,  4
2 (2, 2)
(0, 2)
17. y 2x  5
x
(− 2, 0) 5 10 15 20 y-intercept: y 20 5 5; 0,  5

3 x-intercept: 0 2x  5
13. y
x 5 2x
5; 5,
x 3 2 1 0 1 2 3 x 2 2
0

y 1  32 3 Undef. 3 3
2
1 18. y 4x2  3
2
y
y-intercept: y 40 3 3; 0, 3
(1, 3)
3 x-intercept: 0 4 x2  3
2 (2, 32 (
1
(3, 1) 3 4 x2
(−3, −1)
x None. y cannot equal 0.
−3 −2 −1 1 2 3
−1

−2 (− 2, − 32 (

INSTRUCTOR
S USE ONLY
1, −3)
(−1,
(−1, − 3))




© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© Cengage Learning. All Rights Reserved.

, 4 Chapter P
NOT FOR SALE
Preparation
paration for Calculus
Calc


19. y x2  x  2 x 2  3x
24. y 2
y-intercept: y 02  0  2 3x  1

y 2; 0,  2 02  3 0
y-intercept: y 2
ª¬3 0  1º¼
x-intercepts: 0 x2  x  2
0 x  2 x 1 y 0; 0, 0

x 2, 1; 2, 0 , 1, 0 x 2  3x
x-intercepts: 0 2
3x  1
20. y 2
x  4x
3
x x3
0 2
y-intercept: y 2
0 40
3
3x  1
y 0; 0, 0 x 0,  3; 0, 0 , 3, 0

x-intercepts: 0 x3  4 x
25. x 2 y  x 2  4 y 0
0 x x2 x 2
y-intercept: 02 y  02  4 y 0
x 0, r 2; 0, 0 , r 2, 0
y 0; 0, 0
21. y x 16  x 2
x-intercept: x 2 0  x 2  4 0 0
y-intercept: y 0 16  0 2
0; 0, 0 x 0; 0, 0

x-intercepts: 0 x 16  x 2
26. y 2x  x2  1
0 x 4 x 4 x
y-intercept: y 20  02  1
x 0, 4,  4; 0, 0 , 4, 0 ,  4, 0
y 1; 0, 1

22. y x 1 x2  1 x-intercept: 0 2x  x2  1

y-intercept: y 0 1 02  1 2x x2  1

y 1; 0, 1 4 x2 x2  1
3x 2 1
x-intercept: 0 x 1 x2  1
1
x 1; 1, 0 x2
3
3
2 x x r
23. y 3
5x  1
3 § 3 ·
x ;¨ , 0 ¸¸
2 0 3 ¨© 3 ¹
y -intercept: y 2; 0, 2
50 1
Note: x  3 3 is an extraneous solution.
2 x
x-intercept: 0
5x  1 27. Symmetric with respect to the y-axis because
0 2 x y x
2
6 x 2  6.
x 4; 4, 0
28. y x2  x
No symmetry with respect to either axis or the origin.

29. Symmetric with respect to the x-axis because
2
y y2 x3  8 x.




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© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
© Cengage Learning. All Rights Reserved.