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Section 3 – Topic 1
Input and Output Values
A function is a relationship between input and output.
Ø Domain is the set of values of 𝑥 used for the input of the
function.
Ø Range is the set of values of 𝑦 calculated from the
domain for the output of the function.
In a function, every 𝑥 corresponds to only one 𝑦.
Ø 𝑦 can also be written as 𝑓 𝑥.
Consider the following function:
For every 𝑥 there is a unique 𝑦
input output
domain range
We also refer to the variables as independent and
dependent. The dependent variable depends on the
independent variable.
Refer to the mapping diagram on the previous page.
Which variable is independent? 𝒙
Which variable is dependent? 𝒚
Consider a square whose perimeter depends on the length of
its sides.
What is the independent variable?
The length of the sides
What is the dependent variable?
The perimeter
How would you represent this situation using function
notation?
Let 𝒍 represent the length of one side.
We can choose any letter to represent a
function, such as 𝑓(𝑥) or 𝑔(𝑥). By using
different letters, we show that we are talking
about different functions.
Try It!
- Mrs. Krabappel is buying composition books for her
classroom. Each composition book costs $ 1. 25.
a. What does her total cost depend upon?
The number of composition books she buys
b. What is the input and output?
Input – The number of composition books
Output – The total cost
c. Write a function to describe the situation.
Let 𝒄 represent the number of composition books.
d. If Mrs. Krabappel buys 24 composition books, it will
cost $ 30. Write this function using function notation.
- Consider the following incomplete mapping diagrams.
a. Complete Diagram A so that it is a function.
b. Complete Diagram B so that it is NOT a function.
c. Is it possible to complete the mapping diagram for
diagram C so it represents a function? If so, complete
the diagram to show a function. If not, justify your
reasoning.
Yes. See diagram.
Diagram A
Diagram B Diagram C
- The cost to manufacture 𝑥 pairs of shoes can be
represented by the function 𝐶 𝑥 = 63 𝑥. Complete the
statement about the function.
If 𝐶( 6 ) = 378 , then pairs of shoes cost
- Which of the following relations is NOT a function?
A { 0 , 5 , 2 , 3 , 5 , 8 , 3 , 8 }
B { 4 , 2 , − 4 , 5 , 0 , 0 , ( 10 , 6 )}
C { 6 , 5 , 4 , 1 , − 3 , 2 , 4 , 2 }
D {(− 3 , − 3 ), ( 2 , 1 ), ( 5 , − 2 ), ( 19 , 3 )}
Answer: C
Section 3 – Topic 2
Representing, Naming, and Evaluating Functions
Consider the function 𝑓 𝑥 = 2
JKL
What are the values of the domain of 𝑓 𝑥?
What are the values of the range of 𝑓 𝑥?
Evaluate 𝑓 𝑥 to find the range for the domain {− 2 , 0 , 2 }.
(O𝟐K𝟏)
O𝟏
(𝟎K𝟏)
𝟏
(𝟐K𝟏)
𝟑
Determine whether the following values are true for the given
function.
(𝟓K𝟏)
𝟔
(O𝟏K𝟏)
𝟎
False True
Try It!
- Consider the function 𝑔 𝑥 = 2
]JKL
. Evaluate 𝑔 𝑥 to find
the range for the domain {− 2 , − 1 , 0 }.
𝟑 O𝟐 K𝟏
O𝟓
𝟑 O𝟏 K𝟏
O𝟐
𝟑 𝟎 K𝟏
𝟏
𝟏
𝟑𝟐
𝟏
𝟒
- Your sister is using your credit card to buy tickets on
TicketBoss for a Taylor Quick concert. There is a $ 5. 00
transaction fee with each order, and tickets cost $ 55. 00.
a. Write a function to describe the situation.
Let 𝒕 represent the number of tickets.
b. Evaluate the total cost function if your sister decides
to buy seven tickets in a single transaction.
c. Your credit card statement shows a $ 225. 00
transaction from TicketBoss. How many tickets did
your sister buy?
𝒈 𝒕 = 𝟓𝟓𝒕 + 𝟓 and 𝒈 𝒕 = 𝟐𝟐𝟓
She bought 𝟒 tickets.
Section 3 – Topic 3
Adding and Subtracting Functions
Let ℎ 𝑥 = 2 𝑥
_
_
Find ℎ 𝑥 + 𝑔(𝑥).
𝟐
𝟐
𝟐
𝟐
𝟐
Find ℎ 𝑥 − 𝑔 𝑥.
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
Let’s Practice!
- Consider the following functions.
_
_
_
a. Find 𝑓 𝑥 − 𝑔 𝑥.
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
b. Find 𝑔 𝑥 − ℎ 𝑥.
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
𝟐
BEAT THE TEST!
- Consider the functions below.
_
_
Which of the following is the resulting polynomial when
𝑓 𝑥 is subtracted from 𝑔(𝑥)?
A − 3 𝑥
_
B − 3 𝑥
_
C 3 𝑥
_
D 3 𝑥
_
Answer: C
Section 3 – Topic 4
Multiplying Functions
Use the distributive property and modeling to perform the
following function operations.
Let 𝑓 𝑥 = 3 𝑥
_
- 4 𝑥 + 2 and 𝑔 𝑥 = 2 𝑥 + 3
Find 𝑓(𝑥) ∙ 𝑔(𝑥).
𝟐
𝟐
𝟐
𝟑
𝟐
𝟐
𝟑
𝟐
𝟑
𝟐
!
Let’s Practice!
- Let ℎ 𝑥 = 𝑥 − 1 and 𝑔 𝑥 = 𝑥
]
_
Find ℎ(𝑥) ∙ 𝑔(𝑥).
𝟑
𝟐
𝟑
𝟑
𝟐
𝟐
𝟒
𝟑
𝟑
𝟐
𝟒
𝟑
𝟐
𝟒
𝟑
𝟐
"
$
(
"
"
$
Try it!
- The envelope below has a mailing label:
a. Let 𝐴 𝑥 = 𝐿 𝑥 ∙ 𝑊 𝑥 − 𝑀(𝑥) ∙ 𝑁(𝑥). Find 𝐴(𝑥).
𝟐
𝟐
𝟐
𝟐
RECEIVED
JUN 03 2011
MR. AL GEBRA
123 INFINITY WAY
POLYNOMIAL, XY 11235
