Lesson Preview
What You'll Learn
v
To write a function
rule given a table or
real-world situation
a
...AndWhy
To write a function rule for
finding profit, as in Example 3
('Þ
1
lnteractive lesson includes ¡nstant
self-check, tutorials, and activities.
Writing Function Rules
You can write a rule for a function by analyzing a table of values. Look for a
pattern relating the independent and dependent variables.
1
exnmple
Write
a.
a
Writing a Rule from a Table
function rule for each table.
x
f(x)
T
5
2
6
J
7
4
8
Ask yourself, "'What can I do to
o
6
Relate f(x) equals x
Writef(x):x+4
a.
Chapter
5
v
T
1
-l
9
6
36
9
81
a
x
5, to 2
: x*
plus
to gel 6,
4
9,
to 6 to get 36,. . .?"
You multiply each x-value times itself to get the /(x) value.
y
y
Relate
Write
is
y
:
equals
:
.r times itself
x;2
*z
function rule for each table'
(x)
b.
x
v
c.
x
v
I
3
I
-1
1
2
z
0
2
4
2
4
J
7
-f
6
J
5
4
2
4
8
4
6
Graphs and Functions
')),
4.
Ask yourself, "'What can I do to 3 to get
A rule for the function
CheckUndersfanding @wrlte
254
x
to get
You add 4 to each x-value to get the /(x) value.
A rule for the function is/(x)
b.
1
Scale Model The exhibit-at the lel1 is a scale model oï a clesktop computer. It
about 20 times the size-oj a norrnal-sized desktop computer.
a. Write a function'rhle to describe this relationship.
1s
Relate larger ið' 20 times normal
Define
write
Let n : length of normal-sized computer.
Let L(n) : lenÊth of larger size shown in museum
L(n\
20
I
i
exhibit.
n
L(n) : 20n desctibes the relationship between the size of the
computer in the exhibit and a hormal-sized computer.
The function rule
b. A space bar on a normal-sized computer is afr in long. About how long is the
space bar in the exhibit?
nnection
L(n) :20'n
L(n) : 20 ' 418 substitute +t for n.
L(n) : Bzt .Simplify.
Museum of Science in
Massachusetts, has an
called The Walk
ComputerrM 2000.
The space bar in the exhibit is about
Chegk
87| in.long.
UndøfStanding @ u. Carpentry A carpenter buys flnishing nails by the pound. Each pound of nails
costs $1.19. Write a function rule to describe this relationship.
b. How much do 12lb
of.
finishing nails cost?
'when you
write a function, the dependent variable is defined in terms of the
independent variable.In Example 3 below, prott depends on the number of
lawns mowed, so proût is a function of the number of lawns mowed.
3
Real-World
ExAMPLE
roblem Solvin
Earnings Suppose you borrow money from a relative to buy a lawn mower that
costs $245. You charge $l-8 to mow a lawn. Write a rule to describe your proflt as
function of the number of lawns mowed.
a
total is $is times lawns. minus cost of
Relate profit
mower
mowed
Define Let
n :
number of lawns mowed.
: total Profit'
245
n
'
Write P(n) :18
The function rule P(n) : l&n - 245 describes your profit as a function of the
Let P(n)
ö
lChgek UndøfStandinq- O
-
number of lawns mowed.
Earnings suppose you buy a word-processing software package for $199.You
charge $15 per hour for word processing. Write a rule to describe your profit as a
function of the number of hours you work.
Lesson
5-4
Writing a Function
Rule 255
EXERCISES
@
For more practice, see Extra Pra
rractice by Example
Examplejl
(page 2C¿)
Match each table withìts rule.
Ly:4*
A.
x
_L
2.y:x-4
B.
3,y:-4-x
x
v
-1
-4
-8
0
-6
-5
-4
L
-3
-4
^
-1
v
a
-L
_J
C.
x
v
-1
-3
-4
-5
-6
0
-12
t
-1,6
2
lVrite a function rule for each table.
4.
x
5.
(x)
1
7.
2
(page 255)
f(x)
1
6.
x
f(x)
0.5
1
0.5
2
6
2
1.5
2
1
J
9
J
2.5
J
1.5
4
12
4
3.5
4
2
x
f(xl
x
v
1
_J
_L
J
-6
-9
4
-12
2
Example
x
8.
9.
x
v
-8
-4
64
-1
-8
-4
0
0
0
0
L
4
4
t6
I
64
1,6
Write a function rule for each situation.
10. the total cost
t(c) ofc ounces of cinnamon if each ounce costs $.79
11. the total distance d(n) traveled after n hours at a constant speed of
45 miles per hour
L2. rhe height f(h) of an object in feet when you know the height
/¿
in inches
13. a worker's earnings e(n) for n hours when the worker's hourly wage is $6.37
14. the area A(n) of a square when you know the length n of a side
15. the volume V(n) of a cube when you know the length n of a side
16. the area
Example 3
(page 255)
A(r) of a circle with radius r
17. Food Costs At a supermarket salad bar, the price of a salad depends on its
weight. Salad costs $.19 per ounce.
a. Write a rule to describe the function.
b. How much would an B-ounce salad cost?
18. Postage ln2002,the price of mailing a letter was $.34 for the first ounce
or part of an ounce and $.21 for each ounce or part of an ounce after the
flrst ounce.
a. Write a rule to describe the function.
b. How much did it cost to mail a 4-ounce letter?
256
Chapter
5
Graphs and Functions
Ð
Write
ooo,tYour skills
a
L9.
$
function rule for each table.
tVtath in
20.
Distande
(m)
Distance
(km)
0.5
500
1".0
1000t
I
1.5
1500
2.0
2000
Centimeters
lnches
¡,
1.
2.54
2
5.08
J
7.62
4
10.16
the Media Use the adyertisement at the left for Exercises 2I-22.
21. a. Write a rule to find the total cost c(ø) lot all the books a person buys
through Book Express. Let ø represent the number of additional books
bought (after the first 6 books).
b. Suppose a person þuys 9 books in all' Find the total cost'
c. Evaluate the function for a 6. What does the output represent?
:
additional books at our
low Club price of $10.00
book.To become a Book
22. A bookstore sells the same books for an avefage price of$6 each.
a. Write a function rule to model the total cost C(b) of books bought at the
bookstore. Let b represent the number of books bought'
b. Evaluate your functionfor b : Iz.What does the output represent?
c. You plan to btty 12 books. what is your average cost per book as a member
of Book ExPress?
d. Is it less expensive to buy 12 books through the club or at the
bookstore? ExPlain.
,}
\
ZS.
first
You may resign your
at any time.
*
Writing What advantage(s) can you see of having
table of values for a function?
Z¿. Water Usage Use the function in the table at
the right.
a. IdentifY the dePendent and
independent variables.
b. Write a rule to describe the function.
c. How many gallons of water would you use
for 7 loads of laundrY?
d. Critical Thinking In one month, you used
442 gallons of water for laundry. How many
loads did You wash?
Make
J
a
function rule instead of a
r
¡Ð
WaterUsed g
for Laundry
load
2 loads
3 loads
102 gallons
4loads
136 qallons
1
çD
i,
26.
*uorngMarh
u
34 gallons
68 gallons
'¡ ¡
table of values for each graph. use the table to write
25.
For help reading
a
a
function rule.
v
x
the
a
1
+
graph and solving
ì
--2
Exercise 25, see
page 260.
11
28.
v
2
1
4
-2
Lesson
5-4
Writing a Function
Rule
257
29. Open-Ended Write a function rule that models a real-world situation.
yout function for an input value and explain what the Qutput represents.
I
Ij
30. Tipping You go oìut to dinner and decide to leave aL5o/o tip for the server.
a. The billJor your meal is å. Write an expression for th1 amount of the tip in
li
@
cnull"ns"
terms of å.
i
b. The total cost c(å) of your meal is the original bill plud the tip. Write a
li
function rule to model this situation
c. Suppose the original bill is $18. Find the cost of your meal with a 15% tip.
Write
a
function rule for each table.
?t
31.
1
1
2
I
-1
-2
-3
-4
27
4
64
34. Truck Rental
33.
0
I
-1
-2
7
27
-3
-4
26
1.
64
A truck rental company charges
63
g44 per day
for renting a
medium-sized truck.There is also a charge of $.38 per mile.
a. Write a function rule c(m) to model the cost of renting a truck for a day and
driving m miles.
b. Evaluate your function rule for m : 70 and m : I20.
c. You return the truck to the rental company and pay $58.44 (excluding tax).
How far did you drive?
d. Suppose you need to rent a truck for two days. You plan to drive 150 miles
each day. How much will this cost?
Connection
Real-Ullorld
ing preserves vegetables
by inhibiting the growth of
Pickl
I
I
I
I
I
bacteria. Pickling requires salt
and acids, such as vinegar.
35. Making Pickles The table at the right
shows the relationship between the
amount of pickling salt added to a
gallon of water and the brine
concentration, which is the percent
of salt by weight.
a. Write a function rule to describe
the relationship between salt
volume and brine concentration.
b. Write a function rule to describe
the relationship between salt
weight and brine concentration.
Brine Strength
1
J.J
2.37
4.95
3.465
3
6.6
4.62
4
7.425
5.1975
1
9.9
6.93
J
L
z
2
I
rl
lt
ti
tl
6)@ (Þ
6)(D
il
I
Standardized Test
l
I
Multiple Choice
36. What is the function rule
costs $ 1 1.95?
: 11.9sb
c.r(b):11.95 b
A. r(b)
for the total cost f(b) of b books, if each book
B. r(b)
:
b + 11.9s
D.r(b):b-11.95
37. What is the
function rule for the amount of change C(x) you receive from
you
bill
if
buy x pounds of dog food at $t.00 a pound?
$50
:
H. C(x) :
F. C(x)
258
Chapter
5
Graphs and Functions
- 50
50 - 1.6x
1.6x
G. C(x) : 50x
l.
C(x)
:
160
-
1.6
50x
a
\ Reading
I
Math
kead
)
7 ¡¡
a Èraph
Fon Use WnN ExeRcrse25,Pea,t 257
tþe problem below wilt help you recognize patterns in numeric{l data.These dafa
descibe the coordinates of points on fhe graph of a line. Read and solve the
as you follow along. Check yo,rr,rrrd"r.tanding with the bxercise at the
bottom of the page.
p*dbl"-
Make a table of values for the
graph. Use the table to write a
function rule.
2
v
To create a table from a graph, identify the cooriinates of points on the graph. For
each point,list the x-value in the left column, and the corresponding/(x)-value (or
y-value) in the right column.
*2+
+2
l-r
o Look for patterns between x-values and their
+L
ot 9o
+2
2
+2
4
+1
!r
corresponding y-values.
.
+1
)¡
Look for patterns between consecutive x-values
and between consecutive y-values
To write a function rule from a table, you need to find a pattern among the data.
You can ask yourself,
What do I need to do to x to getf(x)?
Make a guess using one pair of data points. Then try your guess with another pair to see
if it works.The numbers in red in the table show that the difference between x and f(x)
values are not the same. So you cannot add the same number to an x value to get the
corresponding
/(x)
value.
As you go down the table, you can
see
that
as
x-values increase by 2,the corresponding
y-valuesincreasebyl.Noticethatif youmultiply ¿by+youget-1,and(-2,-1)isan
(x, y) pair in the table. Using mental math, you can see that j times any x-value gives the
corresponding y-value.
flxl
equals
r uuftiplied
by
flxl = 2 x
i
Retate.
Write.
EXERC¡SE
2
Make a table of values for the graph.
Use the table to write a function rule.
3
ì
260
Reading
Math
Reading a Graph