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Sec 1.3 New functions from old functions Subtitle
Transformation of functions: Shift a graph of a function
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Sketch the graph: y=|x-2|-1
Scaling and reflecting a graph of a function
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Sketch 1. f(x)=𝑥2 + 6𝑥 + 10 2. y= 1-sin 2x
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
Combination of Functions
• Sums, Differences, Products, and Quotients
Two functions f and g can be combined to form new functions f + g,
f - g, f g and f / g in an manner similar to the way we add, subtract, multiply, and divide real numbers.
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Publishing as Pearson Addison-Wesley
Examples: ,
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( )f x x ( ) 2g x x
Write f/g and find the domain.
Composite function
• If the domain of f is A, and the domain of g is B, then the domain of is
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f g
( ) ( )D f g x B g x A
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Publishing as Pearson Addison-Wesley
Example
• If , find the composite of and
.
• Normally
Copyright © 2008 Pearson Education, Inc.
Publishing as Pearson Addison-Wesley
2( ) , ( ) 3f x x g x x f g
g f
f g g f
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