TEST BANK FOR Calculus 8th Ed (3 Volume Set) By Ron Larson, Robert P. Hostetler and Bruce H. Edwards

Section P.1 Graphs and Models
Solutions to Odd-Numbered Exercises
2
1.
x-intercept:
y-intercept:
Matches graph (b)
0, 2
4, 0
y 12
x 2 3.
x-intercepts:
y-intercept:
Matches graph (a)
0, 4
2, 0, 2, 0
y 4 x2
5.
x
2
2
−4
−6
−8
4
6
8
−8 −6 −4 4 6 8
(−4, −5)
(−2, −2)
(0, 1)
(2, 4)
(4, 7)
y
y 32
x 1 7.
x
2
−4
−2
−6
6
−6 −4 4 6
(−3, −5) (3, −5)
(−2, 0)
(0, 4)
(2, 0)
y
y 4 x2
x 0 2 4
y 5 2 1 4 7
4 2 x 0 2 3
y 5 0 4 0 5
3 2
9.
x
2
−2
4
6
−6 −4 2
(−3, 1) (−1, 1)
(−4, 2)
(−2, 0)
(0, 2)
(1, 3)
(−5, 3)
y
y x 2 11.
x
4
6
8
2
−6
−8
−4
−10
10
−2 2 12 14 16 18
(0, −4)
(1, −3)
(4, −2) (16, 0)
y
(9, −1)
y x 4
x 0 1
y 3 2 1 0 1 2 3
5 4 3 2 1 x 0 1 4 9 16
y 4 3 2 1 0
Section P.1 Graphs and Models 3
13.
Note that y 4 when x 0.
Xmin = -3
Xmax = 5
Xscl = 1
Ymin = -3
Ymax = 5
Yscl = 1
15.
(a)
(b) x, 3 4, 3 3 5 4
2, y 2, 1.73 y 5 2 3 1.73
−6 6
−3
5
(−4.00, 3)
(2, 1.73)
17.
y-intercept:
x-intercepts:
x 2, 1; 2, 0, 1, 0
0 x 2x 1
0 x2 x 2
y 2; 0, 2
y 02 0 2
y x2 x 2 19.
y-intercept:
x-intercepts:
x 0, ±5; 0, 0; ±5, 0
0 x25 x5 x
0 x225 x2
y 0; 0, 0
y 0225 02
y x225 x2
21.
y-intercept: None. x cannot equal 0.
x-intercepts:
x 4; 4, 0
0 2 x
0
32 x
x
y
32 x
x
23.
y-intercept:
x-intercept:
x 0; 0, 0
x20 x2 40 0
y 0; 0, 0
02y 02 4y 0
x2y x2 4y 0
25. Symmetric with respect to the y-axis since
y x2 2 x2 2.
27. Symmetric with respect to the x-axis since
y2 y2 x3 4x.
29. Symmetric with respect to the origin since
xy xy 4.
31.
No symmetry with respect to either axis or the origin.
y 4 x 3
33. Symmetric with respect to the origin since
y
x
x2 1
.
y
x
x2 1
35. is symmetric with respect to the y-axis
since y x3 x x3 x x3 x.
y x3 x
37.
Intercepts:
Symmetry: none
23
, 0, 0, 2
0
y
2 (0, 2)
1
x
1 2 3
1
, 23
y 3x 2
4 Chapter P Preparation for Calculus
39.
Intercepts:
Symmetry: none
x
8 10
(8, 0)
y
2 4
, 4)
2
(
2
0
2
8
6
10
8, 0, 0, 4
y
x
2
4 41.
Intercepts:
Symmetry: y-axis
x
(1, 0)
0, 1)
y
2
( 1, 0)
(
1
2
−2 2
1, 0, 1, 0, 0, 1
y 1 x2 43.
Intercepts:
Symmetry: none
x
2
−2
8
10
12
−10 −8 −6 (−3, 0) 2 4
(0, 9)
y
3, 0, 0, 9
y x 32
45.
Intercepts:
Symmetry: none
y
5
4
3
3
x
2 3
,
1
1
1
,
3 2
( 2 0) (0 2)
3 2, 0, 0, 2
y x3 2 47.
Intercepts:
Symmetry: none
Domain:
x
1
2
3
4
5
−2
6
−4 −3 −1 1 2 3 4
(−2, 0) (0, 0)
y
x ≥ 2
0, 0, 2, 0
y xx 2 49.
Intercepts:
Symmetry: origin
x
1
−2
−3
−4
2
3
4
−4 −3 −2 −1 2 3 4
(0, 0)
y
0, 0
x y3
51.
Intercepts: none
Symmetry: origin
y
3
1
2
x
1 2 3
y
1
x
53.
Intercepts:
Symmetry: y-axis
0, 6, 6, 0, 6, 0
x
2
2
−4
−2
−6
−8
4
6
8
−8 −4 −2 4 6 8
(−6, 0)
(0, 6)
(6, 0)
y 6 x y
55.
Intercepts:
Symmetry: x-axis
0, 3, 0, 3, 9, 0
1
−4
−11
4
(−9, 0)
(0, −3)
(0, 3)
y ±x 9
y2 x 9
y2 x 9 57.
Intercepts:
Symmetry: x-axis
6, 0, 0, 2, 0, 2
8
−3
−1
3
(6, 0)
(0 , 2 )
( 0 , − 2 )
y ±2
x
3
3y2 6 x
x 3y2 6
Section P.1 Graphs and Models 5
59. y x 2x 4x 6 (other answers possible) 61. Some possible equations:
y 3 x
y 3x3 x
y x3
y x
63.
The corresponding y-value is
Point of intersection: 1, 1
y 1.
1 x
3 3x
2 x 2x 1
2x y 1 ⇒y 2x 1
x y 2 ⇒y 2 x 65.
The corresponding y-value is
Point of intersection: 5, 2
y 2.
x 5
5x 25
14 2x 3x 11
7 x
3x 11
2
3x 2y 11 ⇒y
3x 11
2
x y 7 ⇒y 7 x
67.
The corresponding y-values are (for )
and (for ).
Points of intersection: 2, 2, 1, 5
y 5 x 1
y 2 x 2
x 2, 1
0 x 2x 1
0 x2 x 2
6 x2 4 x
x y 4 ⇒y 4 x
x2 y 6 ⇒y 6 x2 69.
The corresponding y-values are and
Points of intersection: 1, 2, 2, 1
y 2 y 1.
x 1 or x 2
0 2x2 2x 4 2x 1x 2
5 x2 x2 2x 1
5 x2 x 12
x y 1 ⇒y x 1
x2 y2 5 ⇒y2 5 x2
71.
The corresponding y-values are and
Points of intersection: 0, 0, 1, 1, 1, 1
y 1.
y 0, y 1,
x 0, x 1, or x 1
xx 1x 1 0
x3 x 0
x3 x
y x
y x3 73.
−4 6
−8
4
y = −x 2 + 3x − 1
y = x 3 − 2x 2 + x − 1
(2, 1)
(0, −1)
(− 1 , −5)
1, 5, 0, 1, 2, 1
x 1, 0, 2