Transformations

x f(x)

   

   

   

   

   

   Domain:

Range:

5 5x

3 4y

Transformations

( )f x k

( )f x k

Vertical Shifts (or Slides)

moves the graph of f(x) up k units. (add k to all of the y-values)

moves the graph of f(x) down k units. (subtract k from all of the y-values)

Transformations

1) Graph ( ) 3f x

Trans:

Domain:

Range:

5 5x Domain:

Range: 3 4y

Transformations

2) Graph ( ) 2f x

Trans:

Domain:

Range:

5 5x Domain:

Range: 3 4y

Transformations

( )f x h

( )f x h

Horizontal Shifts (or Slides)

moves the graph of f(x) right h units. (add h to all of the x-values)

moves the graph of f(x) left h units. (subtract h from all of the x-values)

Transformations

3) Graph ( 2)f x

Trans:

Domain:

Range:

5 5x Domain:

Range: 3 4y

Transformations

4) Graph ( 1)f x

Trans:

Domain:

Range:

5 5x Domain:

Range: 3 4y

Transformations

( )f x

( )f x

Vertical Reflection.

is a reflection of the graph over the x-axis. (Multiply the y-values by -1)

is a reflection of the graph over the y-axis. (Multiply the x-values by -1)

Horizontal Reflection.

Transformations

5) Graph

Trans:

Domain:

Range:

5 5x Domain:

Range:

( )f x

3 4y

Transformations

6) Graph

Trans:

Domain:

Range:

5 5x Domain:

Range:

( )f x

3 4y

Transformations

1)

Trans:

Domain:

Range:

4 6x Domain:

Range: 4 4y

( 1) 2f x

Transformations

2)

Trans:

Domain:

Range:

4 6x Domain:

Range: 4 4y

( 1)f x

Transformations

3)

Trans:

Domain:

Range:

4 6x Domain:

Range: 4 4y

( ) 1f x

Transformations

4)

Trans:

Domain:

Range:

4 6x Domain:

Range: 4 4y

1 3f x