©1999 by Design Science, Inc. Pre-Calculus Lesson 2: Algebra of Functions.

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Presentation transcript:

©1999 by Design Science, Inc. Pre-Calculus Lesson 2: Algebra of Functions

©1999 by Design Science, Inc. 2 Basic function operations  Sum  Difference  Product  Quotient x x

©1999 by Design Science, Inc. 3 Composition of functions  Composition of functions is the successive application of the functions in a specific order.  Given two functions f and g, the composite function is defined by and is read “f of g of x.”

©1999 by Design Science, Inc. 4 A different way to look at it… Function Machine x Function Machine g f

 Evaluate and :  ©1999 by Design Science, Inc. 5 Example

 Evaluate and :  ©1999 by Design Science, Inc. 6 Example

 Evaluate and :  ©1999 by Design Science, Inc. 7 Example

 Evaluate and :  ©1999 by Design Science, Inc. 8 Example You can see that function composition is not commutative!

©1999 by Design Science, Inc. 9 THE DIFFERENCE QUOTIENT

©1999 by Design Science, Inc. 10 THE DIFFERENCE QUOTIENT

©1999 by Design Science, Inc. 11 Example: Given f(x)=3x-7, find

©1999 by Design Science, Inc. 12 Example: Given f(x)=3x-7, find

©1999 by Design Science, Inc. 13 Example: Given f(x)=3x-7, find

©1999 by Design Science, Inc. 14 Example: Given f(x)=3x-7, find

©1999 by Design Science, Inc. 15

©1999 by Design Science, Inc. 16

©1999 by Design Science, Inc. 17

©1999 by Design Science, Inc. 18

©1999 by Design Science, Inc. 19

©1999 by Design Science, Inc. 20

©1999 by Design Science, Inc. 21 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 22 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 23 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 24 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 25 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 26 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 27 Example: f(x) = 3x 2 - 4x - 5

©1999 by Design Science, Inc. 28

©1999 by Design Science, Inc. 29

©1999 by Design Science, Inc. 30

©1999 by Design Science, Inc. 31

Practice: For the function f(x)=2x 2 + 3, find: a)f(2) b)f(t) c)f(x+h) d) ©1999 by Design Science, Inc. 32

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