exercises on transformations
TRANSCRIPT
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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