pokharel (yp624) – HW01 – Radin – (56520)
2
3.
A and B only
correct
4.
B and C only
5.
C only
6.
B only
7.
all of them
8.
A and C only
Explanation:
A. TRUE: by the known product,
(
x
+
y
)
2
=
x
2
+ 2
xy
+
y
2
.
On the other hand,
r
(
x
+
y
)
2
=

x
+
y

,
so if
x
+
y >
0,
x
+
y
=
R
x
2
+ 2
xy
+
y
2
.
But if
a, b
are positive we can set
x
=
√
a
and
y
=
√
b
. The result follows since
x
and
y
are
then positive.
B.
TRUE: by the known diFerence of
squares factorizaation,
x
2
−
y
2
= (
x
−
y
)(
x
+
y
)
.
But if
a, b
are positive we can set
x
=
√
a
and
y
=
√
b
. The result follows after division.
C. ±ALSE:
r
(
x
+
y
)
2
=

x
+
y

,
and since
R
(
·
) is always nonnegative, the
right hand side has to be nonnegative. But
if
a, b
can be positive or negative, an absolute
value sign is then needed on the right.
keywords: square root, properties of square
root, PlaceUT, True±alse, T/±,
004
10.0 points
±ind the domain and range of the function
h
(
x
) =
R
9
−
x
2
.
1.
domain = [0
,
3]
,
range = [3
,
3)
2.
domain = [
−
3
,
3]
,
range = [0
,
3]
cor
rect
3.
domain = [0
,
3]
,
range = [0
,
3]
4.
domain = (
−
3
,
3)
,
range = (0
,
3)
5.
domain = [
−
3
,
3]
,
range = [
−
3
,
3]
6.
domain = (
−∞
,
∞
)
,
range = [0
,
∞
)
Explanation:
If we write
y
=
R
9
−
x
2
, then
x
2
+
y
2
= 9
whose graph is a circle centered at the origin
having radius 3. Thus the graph of
h
is the
upper semicircle shown in
−
3
3
3
Consequently,
h
has
domain = [
−
3
,
3]
,
range = [0
,
3]
.
keywords: range, range of function, circle,
domain, domain of function,
005
10.0 points
There is a linear relationship
T
F
=
mT
C
+
b
between the temperature
T
F
on the ±ahren
heit scale and its equivalent
T
C
on the Centi
grade scale. As the thermometers