Algebra
Lesson 3.14 – 3.16
Name: ___________________________________________
What is a Function Notation?
Notation can be defined as a system of symbols or signs that denote elements such as
phrases, numbers, words etc.
Therefore, function notation is a way in which a function can be represented using
symbols and signs. Function notation is a simpler method of describing a function without
a lengthy written explanation.
Example 1:
As a fundraiser, Manuel is selling tickets to the school play. He has already sold $20 worth
of tickets and the tickets cost $2.50.
Define your variables.
Write an equation to model the total
amount collected from ticket sales.
Let 𝑡 =____________________________
Let C(𝑡) =_________________________
What does C(5) mean in terms of the
situation?
What does C(9) mean in terms of the
situation?
Find C(5).
Find C(9).
What does C(0) mean in terms of the
situation?
What does C(𝑡) = 50 mean in terms of the
situation?
Find C(0).
Find C(𝑡) = 50.
1
Algebra
Lesson 3.14 – 3.16
Example 2:
A lawyer’s fee is $180 per hour for his services.
Define your variables.
Write an equation to model the total charge
after h hours of service.
Let h=____________________________
Let 𝑓(ℎ) =_________________________
What does 𝑓(5) mean in terms of the
situation?
What does 𝑓(20) mean in terms of the
situation?
Find 𝑓(5).
Find 𝑓(20).
What does 𝑓(0) mean in terms of the
situation?
What does 𝑓(𝑡) = 6300 mean in terms of
the situation?
Find 𝑓(0).
Find 𝑓(𝑡) = 6300
Will you ever have a negative number as an output? Does 𝑓(𝑡) = −1700 make sense?
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Algebra
Lesson 3.14 – 3.16
Example 3: Given the following functions, for the unknown values.
Given 𝑓(𝑥) = 2𝑥 − 5, find the following.
a. 𝑓(8)
b. 𝑓(𝑥) = −9
c. 𝑓(16)
d. 𝑓(𝑥) = 15
e. 𝑓(−4)
f. 𝑓(𝑥) = 43
Example 4:
Given 𝑔(𝑥) = −7𝑥 + 9, find the following.
a. 𝑔(3)
b. 𝑔(𝑥) = −19
c. 𝑔(10)
d. 𝑔(𝑥) = 0
e. 𝑔(−5)
f. 𝑔(𝑥) = 58
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Algebra
Lesson 3.14 – 3.16
Example 5:
The Mid-Atlantic Ridge separates the North and South American Plates from
the Eurasian and African Plates. The function graphed relates the number of centimeters
of spread, 𝑆(𝑡) after t years.
What does 𝑆(0) mean in terms of the
situation?
Find 𝑆(0).
What does 𝑆(4) mean in terms of the
situation?
What does S(8.5) mean in terms of the
situation?
Find 𝑆(4).
Find 𝑆(8.5).
What does 𝑆(𝑡) = 6 mean in terms of the
situation?
What does 𝑆(𝑡) = 14 mean in terms of
the situation?
Find 𝑆(𝑡) = 6.
Find 𝑆(𝑡) = 14.
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Algebra
Lesson 3.14 – 3.16
Example 6:
Joshua is driving to the store. The average distance d in miles he travels over t minutes is
given by the function 𝑑(𝑡).
What does 𝑑(0)mean in terms of the
situation?
Find 𝑑(0).
What does 𝑑(1) mean in terms of the
situation?
What does 𝑑(5) mean in terms of the
situation?
Find 𝑑(1).
Find 𝑑(5).
What does 𝑑(𝑡) = 2 mean in terms of the
situation?
What does 𝑑(𝑡) = 3.5 mean in terms of
the situation?
Find 𝑑(𝑡) = 2.
Find 𝑑(𝑡) = 3.5.
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Algebra
Lesson 3.14 – 3.16
Example 7:
1
Given 𝑓(𝑥) = 𝑥 + 8, find the following.
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a. 𝑓(3)
b. 𝑓(𝑥) = −12
c. 𝑓(11)
d. 𝑓(𝑥) = 0
e. 𝑓(−18)
f. 𝑓(𝑥) = 22
Example 8:
Given 𝑔(𝑥) = 6𝑥 − 12, find the following.
a. 𝑔(3)
b. 𝑔(𝑥) = −24
c. 𝑔(10)
d. 𝑔(𝑥) = 0
e. 𝑔(−5)
f. 𝑔(𝑥) = 90
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