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7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
Some Common Functions and Their GraphsSketch the graph of each function. Be sure to label at least 3 key points!
1)Linear Functions bmxxf bxf
2)Power Functions 2xxf 3xxf
4xxf 5xxf
x y x yx y
x y x y
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
3)Root Functions xxf 3 xxf
4
xxf 5
xxf
4)Reciprocal Functions
xxf
1 2
1
xxf
x yx y
x y x y
x y
x y
x y
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
5)Absolute Value Function xxf
x y
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
A. Transformation Rules
1. Sketch a graph of the function.
a. 2 5f x x
b. 5f x x
Vertical ShiftsAdding a constant, c, to a function will shift the graph c units vertically.
f x c shifts the graph c units up f x c shifts the graph c units down
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
c. 4f x x
d. 33f x x
Horizontal ShiftsAdding a constant, c, inside the rule of a function will shift the
function c units horizontally. NOTE: The direction of movement is the
opposite sign!
f x c shifts the graph c units left f x c shifts the graph c units right
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
e. 2f x x
f.
f x x
ReflectionsMultiplying the function by a negative results in either anx-axis ory-
axis reflection.
f x results in anx-axis reflection f x results in ay-axis reflection
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
g. 3f x x
h. 13
f x x
Vertical Stretching and CompressionsMultiplying the function by a constant, c, results in a vertical stretch
or a vertical compression
cf x results in a vertical stretch ifc >1. cf x results in a vertical compression if0 < c < 1 (or if c is a
fraction).
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
i. xxf 2
j. xxf 31
Horizontal Stretching and CompressionsThis occurs when you see a value multiplied byx inside of the function.
0, aaxf results in a horizontal stretch if0 < a < 1 (or if a is afraction).
0, aaxf results in a horizontal compression ifa > 1. To graph this, multiply eachx-coordinate of the function by
a
1.
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
B. Sketch the graph of the function, not by plotting
points, but by starting with the graph of a standard
function and applying transformations.
1.
2.
3( ) 4 5g x x a. What is the common function?
b. Describe the sequence of transformations.
a. What is the common function?
b. Describe the sequence of transformations.
2
( ) 3 2g x x
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
3.
4.
5.
a. What is the common function?
b. Describe the sequence of transformations.
a. What is the common function?
b. Describe the sequence of transformations.
( ) 5 2g x x
( ) 2 4 3g x x
a. What is the common function?
b. Describe the sequence of transformations.
( ) 5 1g x x
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
6.
7.
8.
a. What is the common function?
b. Describe the sequence of transformations.
a. What is the common function?
b. Describe the sequence of transformations.
a. What is the common function?
b. Describe the sequence of transformations.
21
( ) 3 12
g x x
( ) 2 3g x x
( ) 4g x x
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
C. A function fis given, and the indicated transformations are
applied to its graph. Write the equation for the final
transformed graph.
1. 3
f x x ; shifted 2 units to the left and shift upward 3 units
2. f x x ; shrink vertically by a factor of , shift to the left 1 unit, and
shift downward 4 units.
3. f x x ; shift 3 units to the left, shift upward 1 unit, reflect in thex-
axis.
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
D. The graph of a function fis illustrated. Use the graph off
as the first step toward graphing each of the following
functions: 3) xfxFa 2) xfxGb xfxPc ) 21) xfxHd
xfxQe2
1) xfxgf ) xfxhg 2)
7/27/2019 Lesson 2.6.pdf
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Lesson 2.6 Transformations of Graphs
3) xfxFa 2) xfxGb xfxPc ) 21) xfxHd
xfxQe2
1) xfxgf ) xfxhg 2)
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Lesson 2.6 Transformations of Graphs
3) xfxFa 2) xfxGb xfxPc ) 21) xfxHd
xfxQe2
1) xfxgf ) xfxhg 2)