Transformations of H & K

Unit 2: Properties and Attributes of Functions

Any function can be transformed!

RULES

Vertical Translation, Shifts UP by adding K

Horizontal Translation, Slides right by subtracting h

K just adds to the function valueH lies by changing the location of X

y= 𝑓 (𝑥 )+𝑘

x

y

-5 1

-2 4

0 3

2 2

3 0

4 2

6 0

7 -1

-5 5

-2 9

0 7

2 6

3 4

4 6

6 4

7 3

NEW GRAPH

Domain doesn’t change!

x

y

y= 𝑓 (𝑥 )−𝑘-5 1

-2 4

0 3

2 2

3 0

4 2

6 0

7 -1

-5 -4

-2 -1

0 -2

2 -3

3 -5

4 -3

6 -1

7 -2

NEW GRAPH

Domain doesn’t change!

x

y

-5 1

-2 4

0 3

2 2

3 0

4 2

6 0

7 -1

-4 1

-1 4

1 3

3 2

4 0

5 2

7 0

8 -1

NEW GRAPH

Range doesn’t change!

y= 𝑓 (𝑥−h )

x

y

-5 1

-2 4

0 3

2 2

3 0

4 2

6 0

7 -1

-7 1

-4 4

-2 3

0 2

1 0

2 2

4 0

5 -1

NEW GRAPH

Range doesn’t change!

y= 𝑓 (𝑥+h )

is translated 5 units right and 2 units down.

is translated 4 units to the left and 1 unit up.

From only a description

𝑦= 𝑓 (𝑥−5 )−2

𝑦= 𝑓 (𝑥+4 )+1