exercises on transformations

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    EXERCISES ON

    TRANSFORMATIONS

    16 July 2010

    Mathematics Subject Area

    Homework

    555 6

    Summary

    Exercises

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    Exercises on

    Transformations Homework

    Quiz 7: Transformations

    No Quiz on Quadratic Functions As Models

    Long Test 2: July 23

    Homework

    555 6

    Summary

    Exercises

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    555 6: Evaluation of Functions

    GivenHomework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( ) 12 = xxf

    ( ) 2+= xxg

    ( ) ( )21 gf +

    ( ) ( )21 gf

    ( ) ( )53 gf

    ( )

    ( )3

    6

    g

    f

    ( )( )2fg

    Evaluate the following:

    1.

    2.

    3.

    4.

    5.

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    Summary

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( )Given and , 0. f x a k>

    ( ) ( )xfxg =

    ( ) ( ) g x f x =

    ( ) ( ) if 0 1 g x af x a = <

    horizontalverticalTranslation

    Stretching

    Shrinking

    across they-axis

    across the x-axisReflection

    General FormTransformations

    Order of Transformation: R-S-T

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    Exercises

    1. What transformations are involved in the following?

    Write the order of transformation.

    a.

    b.

    c.

    d.

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( ) ( )2+= xfxa

    ( ) ( ) 92 += xfxb

    ( ) ( ) 125

    1= xfxc

    ( ) ( )xfxd = 3

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    ( ) ( ) 2+= xfxa

    ( ) ( ) 1+= xfxb

    ( ) ( )xfxc =

    ( ) ( )xfxd 4=

    ( ) ( ) 45 += xfxe

    ( ) ( )2+= xfxg

    ( ) ( ) 11+= xfxh

    Exercises

    2. Given , determine the following:

    a. domain of

    b. range of

    c. x-intercept of

    d. y-intercept of

    e. vertex of

    f. axis of symmetry of

    g. direction of opening of

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( ) ( ) 12 2 ++= xxf

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    ( ) ( )a x f x =

    ( ) ( )2 3b x f x = +

    ( ) ( )1

    1

    5

    c x f x =

    ( ) ( )4d x f x = +

    Exercises

    3. If the point is on the graph off, what is its

    corresponding point in the graph of

    a.

    b.

    c.

    d.

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( )3,5

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    ( )g x

    Exercises

    4. Given . What is the equation of if

    f is

    a. reflected across the x-axis and shifted 2 units tothe right

    b. stretched by a factor of 4, shifted munits down

    andp units to the left

    c. reflected across they-axis, shrunk by a factor of

    3 and shifted 1 unit up

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( ) 2 3 f x x =

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    Exercises

    5. Given the graph offbelow, determine the graph of

    the following.

    a.

    b.

    c.

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( ) ( ) 2 g x f x = +

    ( ) ( )1 12

    h x f x =

    ( ) ( )1 j x f x =

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    Answer Key

    1.

    a. reflection across the x-axis, shift of 2 units to the

    right

    b. reflection across they-axis, stretching by a factor

    of 2, shift of 9 units upward

    c. reflection across the x-axis, shrinking by a factor

    of 3, shift of 2 units to the right, shift of 1 unit

    downward

    d. reflection across they-axis, shift of 3 units to the

    right

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

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    Answer Key

    2.

    a.

    b.

    c.

    d.

    e.

    f.

    g. upward

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    { }Rx|x

    ( ) ( ){ }0xh|xh

    31,

    12

    ( )53,

    4=x

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    Answer Key

    3.

    a.

    b.

    c.

    d.

    4.

    a.

    b.

    c.

    Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    ( )53 ,

    ( )133,

    ( )23 ,

    ( )57,

    ( ) ( )( ) ( ) 3232 22 +== xxxg

    ( ) ( )( ) ( ) mpxmpxxg +=+= 12434 22

    ( ) ( )( ) 223

    113

    3

    1xxxg =+=

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    Answer Key

    5.Homework

    Exercises on

    Transformations

    555 6

    Summary

    Exercises

    g

    h

    j