© 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.
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
N
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IN
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©
Cengage Learning. All Rights Reserved.
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.
CHAPTER P
Preparation for Calculus
Section P.1 Graphs and Models
1.
3
2
3yx
x-intercept: (2, 0)
y-intercept: (0, 3)
Matches graph (b).
2.
2
9yx
x-intercepts:
3, 0 , 3, 0
y-intercept: (0, 3)
Matches graph (d).
3.
2
3yx
x-intercepts:
3, 0 , 3, 0
y-intercept: (0, 3)
Matches graph (a).
4.
3
yx x
x-intercepts:
0,0, 1,0, 1,0
y-intercept: (0, 0)
Matches graph (c).
5.
1
2
2yx
6.
52yx
7.
2
4yx
8.
2
3yx
9. 2yx
x
4 2
0 2 4
y 0 1 2 3 4
x 1 0 1 2
5
2
3 4
y 7 5 3 1 0 1 3
x 3 2 0 2 3
y 5 0 4 0 5
x 0 1 2 3 4 5 6
y 9 4 1 0 1 4 9
x 5 4 3 2 1 0 1
y 3 2 1 0 1 2 3
−2−424
−2
4
6
y
x
(−2, 1)
(−4, 0)
(0, 2)
(2, 3)
(4, 4)
−2−4−6
−2
−4
2
4
8
y
x
(−1, 7)
(0, 5)
(1, 3)
(2, 1)
(3, −1)
(4, −3)
, 0
5
2
(
(
x
2
−4
−2
−6
6
−4−646
(−3, −5) (3, −5)
(−2, 0)
(0, 4)
(2, 0)
y
−6 −4 −2
−2
2
2
4
4
6
6
8
10
y
x
(1, 4)
(2, 1)
(3, 0)
(4, 1)
(5, 4)
(6, 9)
(0, 9)
x
2
−2
4
6
−4−62
(−3, 1)
(−1, 1)
(−4, 2)
(−2, 0)
(0, 2)
(1, 3)
(−5, 3)
y
N
O
T F
O
R
S
ALE
INSTRUCTOR USE ONLY
S
−−
44
T
(4,
(,
3)
)
2
2
(
(
(
(
©
Cengage Learning. All Rights Reserved.
Section P.1 Graphs and Models 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.
10. 1yx
11. 6yx
12. 2yx
13.
3
y
x
14.
1
2
y
x
15. 5yx
(a)
2, 2, 1.73 5 2 3 1.73yy |
(b)
,3 4,3 3 5 4x
16.
5
5yx x
(a)
0.5, 0.5, 2.47y
(b)
, 4 1.65, 4x and
,4 1,4x
17. 25yx
y-intercept:
20 5 5; 0, 5y
x-intercept:
55
22
02 5
52
;,0
x
x
x
18.
2
43yx
y-intercept:
2
40 3 3; 0,3y
x-intercept:
2
2
04 3
34
x
x
None. y cannot equal 0.
x 3
2 1 0 1 2 3
y 2 1 0 1 0 1 2
x 0 1 4 9 16
y 6 5
4
3
2
x 2 1 0 2 7 14
y 0 1 2 2 3 4
x 3 2 1 0 1 2 3
y 1
3
2
3 Undef. 3
3
2
1
x 6
4 3 2 1 0 2
y
1
4
1
2
1 Undef. 1
1
2
1
4
−3 −23
3
4
−2
2
2
−1
1
y
x
(−3, 2)
(−2, 1)
(−1, 0)
(0, −1)
(1, 0)
(2, 1)
(3, 2)
y
x
(0, −6)
(1, −5)
(4, −4)
(9, −3)
(16, −2)
−4481216
−2
−4
−6
−8
2
5101520
2
3
4
5
y
x
(−2, 0)
(−1, 1)
(0, 2)
(2, 2)
(7, 3)
(14, 4)
y
x
(3, 1)
(1, 3)
(−3, −1)
(−1, −3)
−1−2−3 123
−1
−2
1
2
3
2,
3
2
(
(
−2, −
3
2
(
(
−
1123
−
2
−
3
−
4
−
5
2
3
4
5
1
4
−6, −
()
1
2
−4, −
()
1
2
0,
()
1
4
2,
()
(−3,
−
1)
(−1, 1)
y
x
−9
−6
9
6
(−0.5, 2.47)
(1, −4)
−
66
−
3
5
(−4.00, 3)
(2, 1.73)
NOT FOR SALE
Section P.1 Graph
s
Section P.1 Graph
INSTRUCTOR USE ONLY
S
((
−
1
,
1,
−−
3))
S
S
S
©
Cengage Learning. All Rights Reserved.
4 Chapter P Preparation for Calculus
© 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.
19.
2
2yx x
y-intercept:
2
002
2; 0, 2
y
y
x-intercepts:
2
02
021
2, 1; 2, 0 , 1, 0
xx
xx
x
20.
23
4yx x
y-intercept:
23
040
0; 0, 0
y
y
x-intercepts:
3
04
022
0, 2; 0, 0 , 2, 0
xx
xx x
x
r r
21.
2
16yx x
y-intercept:
2
016 0 0;0,0y
x-intercepts:
2
016
044
0, 4, 4; 0, 0 , 4, 0 , 4, 0
xx
xxx
x
22.
2
11yx x
y-intercept:
2
010 1
1; 0, 1
y
y
x-intercept:
2
011
1; 1, 0
xx
x
23.
2
51
x
y
x
20
-intercept: 2 ; 0, 2
50 1
2
-intercept: 0
51
02
4; 4,0
yy
x
x
x
x
x
24.
2
2
3
31
x
x
y
x
y-intercept:
2
2
030
30 1
0; 0, 0
y
y
ªº
¬¼
x-intercepts:
2
2
2
3
0
31
3
0
31
0, 3; 0, 0 , 3, 0
xx
x
xx
x
x
25.
22
40xy x y
y-intercept:
22
0040
0; 0, 0
yy
y
x-intercept:
22
0400
0; 0, 0
xx
x
26.
2
21yx x
y-intercept:
2
20 0 1
1; 0, 1
y
y
x-intercept:
2
2
22
2
2
02 1
21
41
31
1
3
3
3
33
;,0
33
xx
xx
xx
x
x
x
x
r
§·
¨¸
¨¸
©¹
Note: 33x is an extraneous solution.
27. Symmetric with respect to the y-axis because
2
2
66.yx x
28.
2
yx x
No symmetry with respect to either axis or the origin.
29. Symmetric with respect to the x-axis because
2
23
8.yyxx
NOT FOR SALE
p
aration for Calculus
paration for Calc
IN
S
TRU
C
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NLY
©
Cengage Learning. All Rights Reserved.
Section P.1 Graphs and Models 5
© 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.
30. Symmetric with respect to the origin because
3
3
3
.
yx x
yxx
yx x
31. Symmetric with respect to the origin because
4.xy xy
32. Symmetric with respect to the x-axis because
2
2
10.xy xy
33. 43yx
No symmetry with respect to either axis or the origin.
34. Symmetric with respect to the origin because
2
2
40
40.
xy x
xy x
35. Symmetric with respect to the origin because
2
2
1
.
1
x
y
x
x
y
x
36.
2
2
1
x
y
x
is symmetric with respect to the y-axis
because
2
2
2
2
.
1
1
x
x
y
x
x
37.
3
yxx is symmetric with respect to the y-axis
because
3
33
.yx x xxxx
38. 3yx is symmetric with respect to the x-axis
because
3
3.
yx
yx
39. 23yx
2
3
230 2,-intercept
0 2 3 3 2 , -intercept
yy
xx xx
Intercepts:
2
3
0, 2 , , 0
Symmetry: none
40.
2
3
1yx
2
3
3
22
33 2
0 1 1, -intercept
0 1 1 , -intercept
yy
xxxx
Intercepts:
3
2
0, 1 , , 0
Symmetry: none
41.
2
9yx
2
22
9 0 9, -intercept
0 9 9 3, -intercepts
yy
xx x x
r
Intercepts:
0, 9 , 3, 0 , 3, 0
2
2
99yxx
Symmetry:
y-axis
42.
2
221yxxxx
1
2
0 2 0 1 0, -intercept
021 0,,-intercepts
yy
xx x x
Intercepts:
1
2
0, 0 , , 0
Symmetry: none
43.
3
2yx
3
3
33
0 2 2, -intercept
0 2 2 2, -intercept
yy
xx x x
Intercepts:
3
2, 0 , 0, 2
Symmetry: none
(0, 2)
2
1
x
32
−
1
−
1
, 0
2
3
y
(
(
−1
−1
12
2
−2
y
x
3
2
− , 0
()
(0, 1)
y
x
(3, 0)
(0, 9)
(−3, 0)
−2−4−6 246
−2
2
4
6
10
1
2
3−1−2−3
1
3
5
2
4
(0, 0)
1
2
− , 0
()
y
x
y
x
(0, 2)
−2−3123
−1
1
3
4
5
3
(− 2, 0)
NOT FOR SALE
Section P.1 Graph
s
Section P.1 Graph
IN
S
TRU
C
T
O
RU
S
E
O
NLY
©
Cengage Learning. All Rights Reserved.
