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Watch Out!
Evaluating the Function
Remember that
x
is the total
number of teammembers,
so evaluate the function for
x
=
15, not
x
=
13.
2
Apply Operations with Functions
In many real-world modeling situations you
write multiple functions that each represent one aspect of the problem. You can
combine the functions to build a new function that models a different aspect of the
problem.
ROBOTICS
A robotics competition team is preparing for a tournament. The team’s
captain is ordering custom T-shirts for each of the members. The T-shirts cost $8
each, plus a one-time set-up fee of $25. Sales tax on the order is 8%. The team decides
that the members will split the cost of the T-shirts equally, and that the team’s
captain and vice-captain will not have to pay for their shirts.
a.
Write a function
C
(
x
) that represents the total cost of the T-shirts, where
x
is the
number of team members.
8
x
+
25 represents the cost of T-shirts before sales tax. Multiply by 1.08 to find the
total cost after the 8% sales tax is applied.
C
(
x
)
=
(1.08)(8
x
+
25)
Multiply 8x
+
25 by 1.08.
=
(1.08)(8
x
)
+
(1.08)(25)
Distributive Property
=
8.64
x
+
27
Simplify.
So,
C
(
x
)
=
8.64
x
+
27 represents the total cost of the T-shirts for
x
team members.
b.
Write a function
N
(
x
) to represent the number of team members who pay for the
T-shirts.
All of the team members except the captain and vice-captain pay for T-shirts.
So,
N
(
x
)
=
x
-
2.
c.
Find
(
C
_
N
)
(
x
) and explain what this function represents.
(
C
_
N
)
(
x
)
=
C
(
x
)
_
N
(
x
)
Division of functions
=
8.64
x
+
27
_
x
-
2
Substitution
So,
(
C
_
N
)
(
x
)
=
8.64
x
+
27
_
x
-
2
,
x
≠
2. This function represents the dollar amount that
each paying team member will contribute to the cost of the T-shirts.
d.
If the team has 15 members, how much does each paying team member contribute
to the cost of the T-shirts?
(
C
_
N
)
(15)
=
8.64(15)
+
27
__
15
-
2
Evaluate the function for
x
=
15.
≈
12.05
Simplify.
Each paying member of the team contributes $12.05.
Guided Practice
3.
CHEMISTRY
A chemist has 500 grams of a 15% saline solution. She adds
x
grams of
salt to the solution. Write a function
S
(
x
) that represents the number of grams of
salt in the new solution, a function
T
(
x
) that represents the total number of grams
of the new solution, and then find
(
S
_
T
)
(
x
) and explain what this function represents.
Real-World Example 3
Build a New Function
Real-World Link
In a robotics competition,
teams compete to build
robots that can accomplish
a given task. In 2016, about
29,000 students from
40 countries participated
in a robotics competition
in St. Louis.
Source:
U.S. News & World Report
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