Student Solutions Manual for Calculus: A Complete Course – 10th Edition by Adams & Essex – Full Worked Solutions

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CH APTER 1
Preparation for Calculus

Section 1.1 Graphs and Models............................................................................ 2

Section 1.2 Linear Models and Rates of Change................................................. 11

Section 1.3 Functions and Their Graphs.............................................................. 22

Section 1.4 Fitting Models to Data......................................................................34

Section 1.5 Inverse Functions.............................................................................37

Section 1.6 Exponential and Logarithmic Functions............................................ 54

Review Exercises.....................................................................................................63

Problem Solving..................................................................................................... 73




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C H A P T E R 1
Preparation for Calculus
Section 1.1 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  8. y  x  3
2

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

1x 4 (1, 4) (5, 4)
5. y  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)
5 x
x 1 0 1 2 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
2
5, 0
(4,  3)
4




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Section 1.1 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
1 1
y  14  12 1 Undef. 1 2 4
y

y
4

3 5

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


y  
2 (9, 3)
4
(16,  2) (a) 2, y  2, 1.73 52  3  1.73
(4, 4)
(1,  5)
6

8
(0, 6)
(b) x, 3  4, 3 3  5  4 
16. y  x5  5x
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 (14, 4)
(a) 0.5, y  0.5, 2.47

(1, 1)
3 (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  20  5  5; 0, 5
3 x-intercept: 0  2x  5
13. y 
x 5  2x

x 3 2 1 0 1 2 3 x  52; 52 , 0
3
y 1  32 3 Undef. 3 2
1 18. y  4x2  3
2
y
y-intercept: y  40  3  3; 0, 3
(1, 3)
3 x-intercept: 0  4x2  3
2 2, 32
1
(3, 1) 3  4x2
( 3, 1)
3 2 1 1 2 3
x None. y cannot equal 0.
1

2 2,  32
( 1, 3)




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4 Chapter 1 Preparation for Calculus


19. y  x2  x  2 x2  3x
24. y  2
y-intercept: y  02  0  2 3x  1
y  2; 0,  2 02  30
y-intercept: y  2
x-intercepts: 0  x2  x  2 30  1

0  x  2x  1 y  0; 0, 0

x  2, 1; 2, 0, 1, 0 x2  3x
x-intercepts: 0  2
3x  1
20. y  x  4x
2 3 xx  3
0 
y-intercept: y2  03  40
2
3x  1
y  0; 0, 0 x  0, 3; 0, 0, 3, 0

x-intercepts: 0  x3  4x
25. x2 y  x2  4 y  0
0  xx  2x  2
y-intercept: 02 y  02  4 y  0
x  0,  2; 0, 0,  2, 0
y  0; 0, 0
21. y  x 16  x 2
x-intercept: x20  x2  40  0
y-intercept: y  0 16  02  0; 0, 0 x  0; 0, 0

x-intercepts: 0  x 16  x2
26. y  2x  x2  1
0  x 4  x4  x y-intercept: y  20  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 4x2  x2  1
3x2  1
x-intercept: 0  x  1 x2  1
1
x2 
x  1; 1, 0 3
3
x  
2 x
23. y  3
5x  1 3 ; 3 ,
x  0
3  3
2 0
y-intercept: y   2; 0, 2  
50   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
2
0  2 x y  x  6  x2  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  8x.




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