34. (a)
The function is defined for all values of
x
, so the
domain is (
2‘
,
‘
).
(b)
The function is equivalent to
y
5
ˇ
5
x
2
w
, which attains
all nonnegative values. The range is [0,
‘
).
(c)
[
2
8, 8] by [
2
3, 3]
35. (a)
The logarithm requires
x
2
3
.
0, so the domain is
(3,
‘
).
(b)
The logarithm attains all real values, so the range is
(
2‘
,
‘
).
(c)
[
2
3, 10] by [
2
4, 4]
36. (a)
The function is defined for all values of
x
, so the
domain is (
2‘
,
‘
).
(b)
The cube root attains all real values, so the range is
(
2‘
,
‘
).
(c)
[
2
10, 10] by [
2
4, 4]
37. (a)
The function is defined for
2
4
#
x
#
4, so the domain
is [
2
4, 4].
(b)
The function is equivalent to
y
5
ˇ
)
x
w
)
w
,
2
4
#
x
#
4,
which attains values from 0 to 2 for
x
in the domain.
The range is [0, 2].
(c)
[
2
6, 6] by [
2
3, 3]
38. (a)
The function is defined for
2
2
#
x
#
2, so the domain
is [
2
2, 2].
(b)
See the graph in part (c). The range is [
2
1, 1].
(c)
[
2
3, 3] by [
2
2, 2]
39.
First piece: Line through (0, 1) and (1, 0)
m
5
}
0
1
2
2
1
0
}
5
}
2
1
1
}
5 2
1
y
5 2
x
1
1 or 1
2
x
Second piece:
Line through (1, 1) and (2, 0)
m
5
}
0
2
2
2
1
1
}
5
}
2
1
1
}
5 2
1
y
5 2
(
x
2
1)
1
1
y
5 2
x
1
2 or 2
2
x
f
(
x
)
5
h
40.
First piece: Line through (0, 0) and (2, 5)
m
5
}
5
2
2
2
0
0
}
5
}
5
2
}
y
5
}
5
2
}
x
Second piece: Line through (2, 5) and (4, 0)
m
5
}
0
4
2
2
5
2
}
5
}
2
2
5
}
5 2
}
5
2
}
y
5 2
}
5
2
}
(
x
2
2)
1
5
y
5 2
}
5
2
}
x
1
10 or 10
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 Spring '08
 GERMAN
 codomain, Jazz in the Domain

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