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Check Your Understanding
=
Step-by-Step Solutions begin on page R14.
Find (
f
+
g
)(
x
), (
f
-
g
)(
x
), (
f
·
g
)(
x
), and
(
f
_
g
)
(
x
) for each
f
(
x
) and
g
(
x
). Indicate any
restrictions in the domain.
1.
f
(
x
)
=
x
+
2
2.
f
(
x
)
=
x
2
-
5
g
(
x
)
=
3
x
-
1
g
(
x
)
= -
x
+
8
3.
PHOTOGRAPHY
A group of photographers is planning an exhibit of their work. Each
photographer will contribute 5 prints to the exhibit and the cost of framing each print
is $7.85. There is also a flat fee of $200 to rent the room for the exhibit. The
photographers plan to split the cost of the exhibit equally.
a.
Write a function
C
(
x
) that represents the total cost of the exhibit, where
x
is the
number of photographers.
b.
In addition to the photographers, 3 family members offer to participate in sharing
the cost of the exhibit. Write a function
P
(
x
) to represent the number of people who
pay for the exhibit.
c.
Find
(
C
_
P
)
(
x
) and explain what this function represents.
d.
If there are 8 photographers, how much does each photographer contribute to the
cost of the exhibit?
Practice and Problem Solving
Extra Practice is on page R5.
Find (
f
+
g
)(
x
), (
f
-
g
)(
x
), (
f
·
g
)(
x
), and
(
f
_
g
)
(
x
) for each
f
(
x
) and
g
(
x
). Indicate any
restrictions in the domain.
4.
f
(
x
)
=
2
x
5.
f
(
x
)
=
x
-
1
g
(
x
)
= -
4
x
+
5
g
(
x
)
=
5
x
-
2
6.
f
(
x
)
=
x
2
f
(
x
)
=
3
x
g
(
x
)
= -
x
+
1
g
(
x
)
= -
2
x
+
6
8.
f
(
x
)
=
x
-
2
9.
f
(
x
)
=
x
2
g
(
x
)
=
2
x
-
7
g
(
x
)
=
x
-
5
10.
f
(
x
)
= -
x
2
+
6
11.
f
(
x
)
=
3
x
2
-
4
g
(
x
)
=
2
x
2
+
3
x
-
5
g
(
x
)
=
x
2
-
8
x
+
4
12.
BASKETBALL
During a practice session, Dimitri makes 20 free-throw attempts and
makes 60% of the free throws. Then, on his next attempt, he begins a streak in which
he makes
x
free throws in a row.
a.
What do the functions
f
(
x
)
=
12
+
x
and
g
(
x
)
=
20
+
x
represent?
b.
Find
(
f
_
g
)
(
x
) and explain what this function represents.
b.
Find
(
f
_
g
)
(7) and explain what this value represents.
13.
POPULATION
In a particular county, the population of the two largest cities
can be modeled by
f
(
x
)
=
200
x
+
25 and
g
(
x
)
=
175
x
-
15, where
x
is the
number of years since 2010 and the population is in thousands.
a.
What is the population of the two cities combined after any number
of years?
b.
What is the difference in the populations of the two cities?
Examples 1–2
Example 3
Examples 1–2
7
Examples 3
for a
Self-Check Quiz
318
|
Lesson 5-1
|
Operations with Functions