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Functions Defined

Functions You Should Know

Translations

Reflections

Inverses

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Combining Functions

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 UNIT 2 : FUNCTIONS & TRANSFORMATIONS

 LESSON 7: COMBINATIONS OF TRANSFORMATIONS

 

 

 

 

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Text Box: Note that the mapping form tells you exactly what happens to each point on the graph of your function f(x).  In the above example, multiply the x-value by -2 and subtract 1; then multiply the y-value by 2 and subtract 2.
 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

0

0

1

1

4

2

9

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

-4

-1/4

-3

-1/3

-2

-1/2

-1

-1

-1/2

-2

-1/3

-3

-1/4

-4

0

0

1/4

4

1/3

3

1/2

2

1

1

2

1/2

3

1/3

4

1/4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Text Box: In summary, to graph y = af [k(x  m)] + n from the graph of y = f(x), follow these ideas:

	If a < 0, we have a reflection in the x-axis
	If k < 0, we have a reflection in the y-axis
	If 1 < a < 1, we have a vertical compression
	If a > 1 or a < - 1, we have a vertical stretch
	If 1 < k < 1, we have a horizontal stretch, factor 1/k
	If k > 1 or k < - 1, we have a horizontal compression, factor 1/k
	The value of m gives the horizontal translation (shift)
	The value of n gives the vertical translation (shift)
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


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