Lesson I: Operations with Functions

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Algebra IIA
Unit VI: Properties and Attributes of Functions
• Foundational Material
o Prior study of various functions, graphs and equations
o Perform algebraic operations on various expressions
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•
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

o Perform transformations of various functions
o Model real world applications with functions
Goal
 Model real-world data with functions
Perform operations on functions
Why?
To further build a foundation for higher level mathematics
To solve problems in other classes such as chemistry, physics, and biology
Make predictions by modeling data involving time, money, speed, sports, travel, etc.
• Key Vocabulary
o Composition of functions
Lesson I: Operations with Functions
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•
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Add, subtract, multiply and divide functions.
Write and evaluate composition functions.
Combine standard function types using arithmetic operations. (CC.9-12.F.BF.1b)
Compose functions. (CC.9-12.F.BF.1c)
Rules:
(f + g)(x) = ______________________________________________________________
(f – g)(x) = ______________________________________________________________
(fg)(x) = ________________________________________________________________
(f/g)(x) = ________________________________________________________________
(fog)(x) = ________________________________________________________________
Operations with Functions
()
()
Find and simplify the following given that f x = 2x 2 + 4x - 6 and g x = 2x - 2.
(f + g)(x) =
(fog)(x) =
(f – g)(x) =
(fg)(x) =
(gof)(x) =
sd
(f/g)(x) =
(fog)(3) =
()
()
Find and simplify the following given that f x = 5x - 6 and g x = x 2 - 5x + 6.
(f + g)(x) =
(f – g)(x) =
(fog)(x) =
sd
(fg)(x) =
(f/g)(x) =
(gof)(x) =
()
(gof)(2) =
()
Find and simplify the following given that f x = 3x - 4 and g x = x + 2.
(f + g)(x) =
(f – g)(x) =
(fog)(x) =
sd
(fg)(x) =
(f/g)(x) =
(gof)(x) =
(gof)(2) =
You try:
Evaluate given that f(x) = x2 – 1 and g(x) = 2x + 3
1)
f(2)
2)
f(-3)
3)
g(4)
4)
g(-1)
Examples: Find a rule for the following given the functions below…
You try:
f(x) = 4x2 + 3x – 1
g(x) = 6x + 2
h(x) = 6x2 – x – 12
1)
(f + g)(x)
2)
(f – g)(x)
3)
(hj)(x)
4)
h
   x
 j
j(x) = 2x – 3
Evaluate:
5)
(f + j)(2)
6)
(h – g)(1)
7)
(g j)(0)
8)
g
   1
h
Given f(x) = 2x and g(x) = 7 – x, find the following:
9)
f(g(4))
10)
g(f(4))
Assignment: Page 446, 15-32, 39-42
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