sec 1.3 new functions from old functionsmawjj.people.ust.hk/math1013_course/sec1-3.pdf · sec 1.3...

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



Sketch the graph: y=|x-2|-1

Scaling and reflecting a graph of a function



Sketch 1. f(x)=𝑥2 + 6𝑥 + 10 2. y= 1-sin 2x



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.



Examples: ,



( )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



f g

( ) ( )D f g x B g x A

Example

• If , find the composite of and

.

• Normally



2( ) , ( ) 3f x x g x x f g

g f

f g g f

sec 1.3 new functions from old functionsmawjj.people.ust.hk/math1013_course/sec1-3.pdf · sec 1.3...

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