). Otherwise said, the graph of a function cannot have two points
one directly on top of the other, since this would represent the impossible situation that
f
(
X, Y
) =
a
6
=
b
=
f
(
X, Y
).
Chapter 7.3
Ex 7.3.1 (2 pts)
Solution:
We have learned in this course that a linear function
f
:
R
2
!
R
has a very special form:
f
(
X, Y
) =
a
·
X
+
b
·
Y,
for some constants
a, b
2
R
. Thus,
f
(0
,
0) =
a
·
0 +
b
·
0 = 0
.
This means that the point (0
,
0
,
0) is on the graph of the function
f
.
Ex 7.3.2 (0 pts)
2
d) You can simply count the length of the base and leg of the triangle by referencing the coordinate grid show
(faintly, in the background).
Ex 7.3.3 (2 pts)
7.3 Further Exercises
FE 7.3.1 (6 pts)
Solution:
a)
Z
= 5
X
+ 3
Y
b)
Z
= 4
X
+ 1
.
5
Y
c)
Z
=

3
X

Y
3
FE 7.3.2 (6 pts)
Solution:
a)
Δ
Z
Δ
X
= 7
,
Δ
Z
Δ
Y
= 25
b)
Δ
Z
Δ
X
=

2
,
Δ
Z
Δ
Y
= 3
c)
Δ
Z
Δ
X
= 16
,
Δ
Z
Δ
Y
=
⇡
4