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.
This
preview
has intentionally blurred sections.
Sign up to view the full version.
This is the end of the preview.
Sign up
to
access the rest of the document.
- Spring '10
- JAMESDCAMPBELL
- Real Numbers, Level set, Lonesome Mountain
-
Click to edit the document details
