Sec.12.1 Functions of Several Variables
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.
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
Real 3 space such that
z = f(x,y)
and (
x,y
) is in D.
A linear function of two variables is of the form
z = f(x,y) = ax + by + c and graphs the plane
ax + by –z + c = 0.
EX 1 Sketch the graph of
z = 12 4x 3y
.
Since the function graphs a plane, choose the intercepts to graph.
x
y
z
= f(x, y)
0
0
x intercept
0
0
y intercept
0
0
z intercept
EX 2
Let
(, ) l
n
(
1
)
fxy
x y
=+
−
.
A.
Evaluate
f(1, 1)
and
f(e, 1).
B.
Find and sketch the domain of
f
.
C.
Find the range of
f
.
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View Full DocumentThe level curves or contour curves of a function
f
of two variables are the curves with the equations
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 Spring '03
 MECothren
 Set Theory, Real Numbers, Multivariable Calculus, unique real number

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