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by: Monica Chang

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# Calculus 1, Week 6 Notes 21-111

Monica Chang
CMU

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- Graphical transformations - Combinations of functions
COURSE
Calculus 1
PROF.
Deborah Brandon
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Mathematical Sciences

This 1 page Class Notes was uploaded by Monica Chang on Tuesday October 11, 2016. The Class Notes belongs to 21-111 at Carnegie Mellon University taught by Deborah Brandon in Fall 2016. Since its upload, it has received 4 views. For similar materials see Calculus 1 in Mathematical Sciences at Carnegie Mellon University.

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Date Created: 10/11/16
Graphical transformations: y=− f (x)reflectsy= f (x)about x−axis y= f (−x)reflectsy= f (x)aboutthe y−axis y= f (x)+cshiftsy= f (x)¿theupcunits y= f (x)−cshifts y= f (x)¿thedowncunits y= f x+c )shfits y= (x)¿the¿units y= f x−c shfits y= fx ¿the¿cunits y=cf (x)stretches y= f (x)verticallybyc y= ( f (x))compresses y= f (x)verticallybyc c y= f cx compresses y= f (x)horizontally byc 1 y= f ( ) stretchesy= f (x)horizontallybyc c Combinations of functions:  ( f ±g¿ (x)= f (x)±g(x)  (fg)x)= f x g x ) f f(x)  () (x)= provided g(x)≠0 g g( ) f  For (f ±g)(x),(fg)x),∧ (g x , the domain is the intersection of f and g, but for f (x) , make g(x) cannot equal 0. (g  Composite of f & g: (f ∘g)x = f (g(x) o In general, f ∘g≠g∘ f  But f ∘g=g∘ f when  f =g f ∧gundoeachother

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