vasquez (mpv244) – HW01 – Schultz – (56445)
2
3.
all of them
4.
none of them
5.
C only
6.
B and C only
7.
A and C only
8.
A and B only
Explanation:
A.
FALSE:
radicalBig
(
x
+
y
)
2
=

x
+
y

,
and since
radicalbig
(
·
) 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.
B.
TRUE: by the known product,
(
x
+
y
)
2
=
x
2
+ 2
xy
+
y
2
.
On the other hand,
radicalBig
(
x
+
y
)
2
=

x
+
y

,
so if
x
+
y >
0,
x
+
y
=
radicalbig
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.
C.
FALSE: by the known difference of
squares factorization,
x
2
−
y
2
= (
x
−
y
)(
x
+
y
)
.
But if
a, b
are positive we can set
x
=
√
a
and
y
=
√
b
. Thus, after division,
a
−
b
√
a
+
√
b
=
√
a
−
√
b ,
contrary to the assertion.
keywords:
square root, properties of square
root, PlaceUT, TrueFalse, T/F,
004
10.0 points
Find the domain and range of the function
h
(
x
) =
radicalbig
36
−
x
2
.
1.
domain = [0
,
6]
,
range = [0
,
6]
2.
domain = [0
,
6]
,
range = [6
,
6)
3.
domain = (
−∞
,
∞
)
,
range = [0
,
∞
)
4.
domain = [
−
6
,
6]
,
range = [0
,
6]
cor
rect
5.
domain = (
−
6
,
6)
,
range = (0
,
6)
6.
domain = [
−
6
,
6]
,
range = [
−
6
,
6]
Explanation:
If we write
y
=
radicalbig
36
−
x
2
, then
x
2
+
y
2
= 36
whose graph is a circle centered at the origin
having radius 6.
Thus the graph of
h
is the
upper semicircle shown in
−
6
6
6
Consequently,
h
has
domain = [
−
6
,
6]
,
range = [0
,
6]
.
keywords:
range, range of function, circle,
domain, domain of function,