63 / 84
28.
PHYSICS
Johannes Kepler developed the formula
d
=
3
√
6
t
2
, where
d
is the distance of
a planet to the Sun in millions of miles and
t
is the number of Earth days that it takes
for the planet to orbit the Sun.
a.
Use a graphing calculator to graph the function. Explain why the graph of the
function
f
(
t
)
=
3
√
6
t
2
is not the graph of a standard cube root function.
b.
If the length of a year on Venus is 224.7 Earth days, how far is the Sun from Venus?
29.
MODELING
The surface area
S
of a sphere can be determined from the volume of the
sphere using the formula
S
=
3
√
36
π
V
2
, where
V
is the volume.
a.
Use a graphing calculator to graph the function. Explain why the graph of
S
=
3
√
36
π
V
2
is not the graph of a standard cube root function.
b.
Determine the surface area of a sphere with a volume of 200 cubic inches.
Write the cube root function represented by each graph. Points with integer coordinates
are shown, with one point the inflection point.
30.
C05_025A_903990
y
x
O
C05_026A_903990
y
x
O
32.
C05_027A_903990
y
x
O
33.
GEOMETRY
The side length of a cube is determined by
r
=
3
√
V
, where
V
is the volume
in cubic units.
a.
Graph the function.
b.
What is the domain and range of the function? Justify your reasoning.
c.
What is the side length of a cube with a volume of 512 cubic centimeters?
H.O.T. Problems
Use
H
igher-
O
rder
T
hinking Skills
34.
REASONING
Explain how to find an equation for a cube root function that passes
through the points (
-
8,
-
1) if the inflection point is (0, 0).
35.
REASONING
Is the function
f
(
x
)
=
3
√
xodd
,
even
, or
neither
? Explain.
36.
WRITING INMATH
Explain why there are no limitations on the domain and range of a
cube root function.
37.
ERROR ANALYSIS
Lin thinks that the graph and the equation
g
(
x
)
=
3
√
x
, represent the
same function. Milo disagrees. Who is correct? Explain your reasoning.
C05_028A_903990
y
x
O
f
(
x
)
=
x
2
38.
CHALLENGE
Use a graphing calculator to explore the graphs of
f
(
x
)
=
√
x
,
g
(
x
)
=
3
√
x
,
h
(
x
)
=
4
√
x
, and
j
(
x
)
=
5
√
x
. Describe the graph of
s
(
x
)
=
n
√
x
, if
n
is even and if
n
is odd?
31
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