IXL - Describe function transformations (Algebra 1 practice)

What kind of transformation converts the graph of

(

)

(

–

)

–

into the graph of

(

)

–

translation 3 units left

translation 3 units up

translation 3 units right

translation 3 units down

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Learn with an example

question

What kind of transformation converts the graph of

(

)

–

into the graph of

(

)

–

translation 10 units down

translation 10 units right

translation 10 units up

translation 10 units left

key idea

Transformation of f ( x )	Transformation of graph of f ( x )
f ( x + h )	Translate h units left
f ( x – h )	Translate h units right
f ( x ) + k	Translate k units up
f ( x ) – k	Translate k units down

The standard form of an absolute value function is

(

)

–

The vertex is

(

)

solution

Apply the possible translations to

(

)

–

and see which one produces

(

)

–

Translate

(

)

10 units down:

(

)

–

This function is

(

)

So the translation 10 units down of the graph of

(

)

is the graph of

(

)

You could also solve the problem by finding the translation that takes the vertex of

(

)

to the vertex of

(

)

The vertex of

(

)

–

(

–

)

and the vertex of

(

)

–

(

–

)

so the translation 10 units down of the graph

(

)

is the graph of

(

)

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Not feeling ready yet? These can help:

DD.4Dilations of functions

DD.3Reflections of functions

DD.2Translations of functions

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