P1: PBU/OVY
P2: PBU/OVY
QC: PBU/OVY
T1: PBU
JWDD02715
JWDD027Salasv1
December 5, 2006
16:40
758
SECTION 15.1
CHAPTER 15
SECTION 15.1
1.
dom (
f
) = the first and third quadrants, including the axes;
range (
f
) = [0
,
∞
)
2.
dom (
f
) = the set of all points (
x, y
) with
xy
≤
1; the two branches of the hyperbola
xy
= 1 and all
points in between;
range (
f
) = [0
,
∞
)
3.
dom (
f
) = the set of all points (
x, y
) except those on the line
y
=
−
x
;
range (
f
) = (
−∞
,
0)
∪
(0
,
∞
)
4.
dom (
f
) = the set of all points (
x, y
) other than the origin;
range (
f
) = (0
,
∞
)
5.
dom (
f
) = the entire plane;
range (
f
) = (
−
1
,
1) since
e
x
−
e
y
e
x
+
e
y
=
e
x
+
e
y
−
2
e
y
e
x
+
e
y
= 1
−
2
e
x
−
y
+ 1
and the last quotient takes on all values between 0 and 2.
6.
dom (
f
) = the set of all points (
x, y
) other than the origin;
range (
f
) = [0
,
1]
7.
dom (
f
) = the first and third quadrants, excluding the axes;
range (
f
) = (
−∞
,
∞
)
8.
dom (
f
) =the set of all points (
x, y
) between the branches of the hyperbola
xy
= 1;
range (
f
) = (
−∞
,
∞
)
9.
dom (
f
) = the set of all points (
x, y
) with
x
2
< y
—in other words, the set of all points of the plane
above the parabola
y
=
x
2
;
range (
f
) = (0
,
∞
)
10.
dom
(
f
) =
the
set
of
all
points
(
x, y
)
with
−
3
≤
x
≤
3
,
−
1
≤
y
≤
1
(a rectangle);
range (
f
) = [0
,
3]
11.
dom (
f
) = the set of all points (
x, y
) with
−
3
≤
x
≤
3
,
−
2
≤
y
≤
2
(a rectangle);
range (
f
) = [
−
2
,
3]
12.
dom (
f
) = all of space;
range (
f
) = [
−
3
,
3]
13.
dom (
f
) = the set of all points (
x, y, z
) not on the plane
x
+
y
+
z
= 0;
range (
f
) =
{−
1
,
1
}
14.
dom (
f
) = the set of all points (
x, y, z
) with
x
2
=
y
2
—that is, all points of space except for those
which lie on the plane
x
−
y
= 0 or on the plane
x
+
y
= 0;
range (
f
) = (
−∞
,
∞
)
15.
dom (
f
) = the set of all points (
x, y, z
) with

y

<

x

;
range (
f
) = (
−∞
,
0]
16.
dom (
f
) =the set of all points (
x, y, z
) not on the plane
x
−
y
= 0;
range (
f
) = (
−∞
,
∞
)
17.
dom (
f
) = the set of all points (
x, y
) with
x
2
+
y
2
<
9 —in other words, the set of all points of the
plane inside the circle
x
2
+
y
2
= 9;
range (
f
) = [2
/
3
,
∞
)
18.
dom (
f
) = all of space;
range (
f
) = [0
,
∞
)
19.
dom (
f
) = the set of all points (
x, y, z
) with
x
+ 2
y
+ 3
z >
0 — in other words, the set of all points in
space that lie on the same side of the plane
x
+ 2
y
+ 3
z
= 0 as the point (1
,
1
,
1);
range (
f
) = (
−∞
,
∞
)
20.
dom (
f
) = the set of all points (
x, y, z
) with
x
2
+
y
2
+
z
2
≤
4 — in other words, the set of all points
inside and on the sphere
x
2
+
y
2
+
z
2
= 4;
range (
f
) = [1
, e
2
]
21.
dom (
f
) = all of space;
range (
f
) = (0
,
1]