Math 200, Spring 2010
Handout 10
Section 14-1
Functions of Two or More Variables
Definition of a Function
f
of Two Variables and the Graph of
f
A
function
f
of two variables
is a rule that assigns to each ordered pair of real numbers
(
)
,
x y
in a set
D
a unique real number denoted by
(
)
,
f
x y
.
The set
D
is the
domain
of
f
and its
range
is the set of values
that
f
takes on, that is, range =
(
) (
)
{
}
,
|
,
f
x y
x y
D
∈
.
If
f
is a function of two variables with domain
D
, then the
graph
of
f
is the set of all points
(
)
,
,
x y z
in
3
ℝ
such that
(
)
,
z
f
x y
=
and
(
)
,
x y
is in
D
.
The graph of
f
is a surface
S
lying directly above or below its
domain
D
in the
xy
-plane.
1.
Find the domains and ranges of the following functions and sketch their domains.
(a)
(
)
2
,
1
f
x y
x
y
=
+
−
(b)
(
)
(
)
,
ln
f
x y
y
x
y
x
=
−
+
(c)
2
1
( , )
g y z
z
y
=
+
(d)
/
( , )
r s
P r s
e
=
Horizontal and Vertical Traces of the Graph of Function
f
(
x
,
y
)
Traces
are curves obtained by intersecting the graph of a function
(
)
,
f
x y
with planes parallel to a coordinate plane.
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- Spring '10
- JAMESDCAMPBELL
- Real Numbers, Level set, Lonesome Mountain
-
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