34 / 84
EMPLOYMENT
The number of women and men age 16 and over employed each year in
the United States can be modeled by the following equations, where
x
is the number of
years since 2000 and
y
is the number of people in thousands.
women:
y
=
548.6
x
+
66,527
men:
y
=
2090.7
x
+
62,243
a.
Write a function that models the total number of men and women employed in the
United States during this time.
b.
If
f
is the function for the number of men, and
g
is the function for the number of
women, what does (
f
-
g
)(
x
) represent?
If
f
(
x
)
=
x
+
2,
g
(
x
)
= -
4
x
+
3, and
h
(
x
)
=
x
2
-
2
x
+
1, find each value.
40.
(
f
·
g
·
h
)(3)
41.
[(
f
+
g
)
·
h
](1)
42.
(
h
_
fg
)
(
-
6)
43.
MULTIPLE REPRESENTATIONS
You will explore (
f
·
g
)(
x
), and
(
f
_
g
)
(
x
), if
f
(
x
)
=
x
2
+
1
and
g
(
x
)
=
x
-
3.
a. Tabular
Make a table showing values for (
f
·
g
)(
x
) and
(
f
_
g
)
(
x
).
b. Graphical
Use a graphing calculator to graph (
f
·
g
)(
x
) and
(
f
_
g
)
(
x
) on the same
coordinate plane.
c. Verbal
Explain the relationship between (
f
·
g
)(
x
) and
(
f
_
g
)
(
x
).
44.
MULTI-STEP
Ice cream cones are one of many treats sold at Sam’s Desserts. They sell 60
scoops for every gallon of ice cream. They pay $6 per gallon of ice cream, $2 for every
box of 24 cones, and allocate a fixed monthly cost of $400 to ice cream. Their sales
reports for the past 6 months are shown.
Month
January February March
April
May
June
Price
$3.50
$3.70
$3.90
$3.75
$3.55
$3.80
Scoops Sold
224
208
188
205
219
199
a.
What is their maximum monthly profit from ice cream sales?
b.
Describe your solution process.
H.O.T. Problems
Use
H
igher-
O
rder
T
hinking Skills
45.
OPEN-ENDED
Write two functions
f
(
x
) and
g
(
x
) such that (
f
·
g
)(
x
)
=
2
x
2
-
2.
46.
CHALLENGE
Given that (
f
+
g
)(4)
=
8 and (
f
-
g
)(4)
= -
6, find
f
(4) and
g
(4).
47.
REASONING
State whether each statement is
sometimes
,
always
, or
never
true.
Explain.
a.
If
f
(
x
) and
g
(
x
) are linear functions, then there is one value that is excluded from the
domain of (
f
+
g
)(
x
).
b.
If
f
(
x
) and
g
(
x
) are linear functions, then there is one value that is excluded from the
domain of
(
f
_
g
)
(
x
).
48.
STRUCTURE
Suppose
f
(
x
)
=
ax
2
+
bx
+
c
and
g
(
x
)
=
mx
2
+
nx
+
p
, for constants
a
,
b
,
c
,
m
,
n
, and
p
, with
a
≠
0 and
m
≠
0. What can you conclude about the constants if
the domain of
(
f
_
g
)
(
x
) is all real numbers? Explain.
49.
WRITING INMATH
If
f
(
x
) and
g
(
x
) are polynomials, what can you say about the domains
of (
f
+
g
)(
x
), (
f
-
g
)(
x
), (
f
•
g
)(
x
), and
(
f
_
g
)
(
x
)?
39
320
|
Lesson 5-1
|
Operations with Functions