# FUNCTIONS : Translations and Transformations Translation – the “shifting” of a function - PowerPoint PPT Presentation

1 / 23

FUNCTIONS : Translations and Transformations Translation – the “shifting” of a function Transformation – the “stretching” or “shrinking” of a function. Shifts the function left. Shifts the function right. Shifts the function up. Shifts the function down.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

FUNCTIONS : Translations and Transformations Translation – the “shifting” of a function

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

#### Presentation Transcript

FUNCTIONS : Translations and Transformations

Translation – the “shifting” of a function

Transformation – the “stretching” or “shrinking” of a function

Shifts the function left

Shifts the function right

Shifts the function up

Shifts the function down

Stretches / shrinks the function vertically

Stretches / shrinks the function horizontally

FUNCTIONS : Translations and Transformations

The easiest way to describe these is to just show you an example with a few rules :

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = 3x + 2, find ƒ ( x - 3 ) for the given values.

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = 3x + 2, find ƒ ( x - 3 ) for the given values.

** since the change is inside parens, we will add 3 to all x’s

ƒ(x)

ƒ(x - 3)

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = 3x + 2, find ƒ ( x - 3 ) for the given values.

** since the change is inside parens, we will add 3 to all x’s

ƒ(x)

ƒ(x - 3)

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = 3x + 2, find ƒ ( x - 3 ) for the given values.

** notice that y stays the same

ƒ(x)

ƒ(x - 3)

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = x2 - 4, find ƒ ( x ) + 5 for the given values.

** change is outside, so add 5 to y

ƒ(x)

ƒ(x) + 5

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = x2 - 4, find ƒ ( x ) + 5 for the given values.

** change is outside, so add 5 to y

ƒ(x)

ƒ(x) + 5

FUNCTIONS : Translations and Transformations

Rule #1 – if the “change” is outside parentheses, you change the y

coordinate by the exact operation that is given.

Rule #2 – if the “change” is inside parentheses, you change the x

coordinate by the opposite operation that is given

EXAMPLE : ƒ( x ) = x2 - 4, find ƒ ( x ) + 5 for the given values.

** notice that x stays the same

ƒ(x)

ƒ(x) + 5

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) =

• ƒ ( 2x ) =

• ƒ ( x ) – 5 =

• 3 ƒ(x) =

• ½ ƒ(x) =

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) =

• ƒ ( x ) – 5 =

• 3 ƒ(x) =

• ½ ƒ(x) =

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by2

• ƒ ( x ) – 5 =

• 3 ƒ(x) =

• ½ ƒ(x) =

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) =

• ½ ƒ(x) =

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) = ( 3 , - 3 )- outside, change y by multiplying by3

• ½ ƒ(x) =

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) = ( 3 , - 3 )- outside, change y by multiplying by 3

• ½ ƒ(x) = ( 3 , -1/2 )- outside, change y by dividing by 2

• ƒ =

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) = ( 3 , - 3 )- outside, change y by multiplying by 3

• ½ ƒ(x) = ( 3 , -1/2 )- outside, change y by dividing by 2

• ƒ = ( 2 , -1 )- inside, change x by multiplying by 2/3

• ƒ ( x – 6 ) =

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) = ( 3 , - 3 )- outside, change y by multiplying by 3

• ½ ƒ(x) = ( 3 , -1/2 )- outside, change y by dividing by 2

• ƒ = ( 2 , -1 )- inside, change x by multiplying by 2/3

• ƒ ( x – 6 ) = ( 9 , -1 )- inside, change x by adding 6

• ƒ ( x ) + 1 =

FUNCTIONS : Translations and Transformations

• Example : Given the coordinate ( 3 , -1 ), perform each translation

• or transformation.

• ƒ ( x + 2 ) = ( 1 , -1 )- inside, change x by subtracting 2

• ƒ ( 2x ) = ( 3/2 , -1 )- inside, change x by dividing by 2

• ƒ ( x ) – 5 = ( 3 , - 6 )- outside, change y by subtracting 5

• 3 ƒ(x) = ( 3 , - 3 )- outside, change y by multiplying by 3

• ½ ƒ(x) = ( 3 , -1/2 )- outside, change y by dividing by 2

• ƒ = ( 2 , -1 )- inside, change x by multiplying by 2/3

• ƒ ( x – 6 ) = ( 9 , -1 )- inside, change x by adding 6

• ƒ ( x ) + 1 = ( 3 , 0 )- outside, change y by adding 1

FUNCTIONS : Translations and Transformations

Graphing1. Find coordinates for the original function

by picking some x’s

2. Create an x/y table with the “change”

EXAMPLE : Graph ƒ ( x – 4 ) if ƒ(x) = 3x2 - 1

FUNCTIONS : Translations and Transformations

Graphing1. Find coordinates for the original function

by picking some x’s

2. Create an x/y table with the “change”

EXAMPLE : Graph ƒ ( x – 4 ) if ƒ(x) = 3x2 - 1

ƒ(x) = 3x2 - 1

FUNCTIONS : Translations and Transformations

Graphing1. Find coordinates for the original function

by picking some x’s

2. Create an x/y table with the “change”

EXAMPLE : Graph ƒ ( x – 4 ) if ƒ(x) = 3x2 - 1

ƒ(x) = 3x2 - 1

FUNCTIONS : Translations and Transformations

Graphing1. Find coordinates for the original function

by picking some x’s

2. Create an x/y table with the “change”

EXAMPLE : Graph ƒ ( x – 4 ) if ƒ(x) = 3x2 - 1

ƒ( x – 4 )

ƒ(x) = 3x2 - 1

- inside, change x by adding 4

FUNCTIONS : Translations and Transformations

Graphing1. Find coordinates for the original function

by picking some x’s

2. Create an x/y table with the “change”

3. Graph the new coordinate set

EXAMPLE : Graph ƒ ( x – 4 ) if ƒ(x) = 3x2 - 1

ƒ( x – 4 )

ƒ(x) = 3x2 - 1