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PENDULUMS
The period of a pendulum can be represented by
T
=
2
π
√
L
_
g
, where
T
is the time in seconds,
L
is the length in
feet, and
g
is gravity, 32 feet per second squared.
a.
Graph the function for 0
≤
L
≤
10.
b.
What is the period for lengths of 2, 5, and 8 feet?
46.
PHYSICS
Using the function
m
=
m
0
_
√
1
-
(
v
2
_
c
2
)
, Einstein’s theory of relativity states that
the apparent mass
m
of a particle depends on its velocity
v
. An object that is traveling
extremely fast, close to the speed of light
c
, will appear to have more mass compared to
its mass at rest,
m
0
.
a.
Use a graphing calculator to graph the function for a ship that weighs 10,000
kilograms for the domain 0
≤
v
≤
300,000,000. Use 300 million meters per second
for the speed of light.
b.
What viewing window did you use to view the graph?
c.
Determine the apparent mass
m
of the ship for speeds of 100 million, 200 million,
and 299 million meters per second.
H.O.T. Problems
Use
H
igher-
O
rder
T
hinking Skills
47.
CHALLENGE
Write an equation for a square root function with a domain of
{
x
|
x
≥ -
4}, a range of {
y
|
y
≤
6}, and that passes through (5, 3).
48.
REASONING
For what positive values of
a
are the domain and range of
f
(
x
)
=
a
√
x
the set of real numbers?
49.
OPEN-ENDED
Write a square root function for which the domain is {
x
|
x
≥
8} and the
range is {
y
|
y
≤
14}.
50.
WRITING INMATH
Explain why there are limitations on the domain and range of
functions that have inverses that are functions.
51.
ERROR ANALYSIS
Cleveland thinks that the graph and the equation represent the same
function. Molly disagrees. Who is correct? Explain your reasoning.
C07_018A_888482_A
x
2 4 86
−
8
−
6
−
4
8
6
2
y
−
2
−
4
−
6
−
8
O
4
52.
WRITING INMATH
Explain why
y
= ±
√
x
is not a function.
53.
OPEN-ENDED
Write an equation of a relation that contains a radical and its inverse
such that
a.
the original relation is a function, and its inverse is not a function.
b.
the original relation is not a function, and its inverse is a function.
45
y
=
√
5
x
+
10
9
12 1
2
11
5 7
10
4
8
6
3
9
12 1
2
11
5 7
10
4
8
6
3
C07-047A-888482
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