Reteach 5-9

Name
LESSON
5-9
Date
Class
Reteach
Transforming Linear Functions
The function f  x   x is called the parent function for the family of linear functions.
Changing the y-intercept will shift
the line up or down. This is called
a translation.
Changing the slope of a line will
change the steepness of the line.
This is called a rotation.
1x.
Graph f  x   x, g  x   4x, and h  x   __
2
Describe the transformations.
Graph f  x   x, g  x   x  2, and
h  x   x  4. Describe the
transformations.
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line is
steeper
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shift 2 up
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parent
function
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line is less
steep
shift 4 down
The y-intercept of g  x  is 2 so the graph
shifts up 2 units from f  x . The y-intercept of
h  x  is 4 so the graph shifts down 4 units
from f  x .
The slope of g  x  is 4 so the line is steeper
than f  x  which has a slope of 1. The slope
1 and it is less steep.
of h  x  is __
2
�
1. Graph f  x   x and g  x   x  3. Then describe
the transformation from the graph of f  x  to the
graph of g  x .
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Describe the transformations from the graph of f  x  to the
graph of g  x .
��
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1x
2. f  x   x; g  x   __
3
3. f  x   x; g  x   x  5
4. f  x   x; g  x   6x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c05-9_rt.indd 70
70
Holt Algebra 1
12/12/05 7:54:11 PM
Name
LESSON
5-9
Date
Class
Reteach
Transforming Linear Functions (continued)
When the slope of a line is multiplied
by 1, the graph is reflected across the
y-axis. This is called a reflection.
More than one transformation can be applied
to a linear function.
Graph f  x   x and g  x   2x  3. Then
describe the transformations from the
graph of f  x  to the graph of g  x .
Graph g  x   4x. Then reflect the graph
of g  x  across the y-axis. Write a function
h  x  to describe the new graph.
�
�
The graph
is steeper
and shifted
3 units
down.
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The y-axis
is a line of
symmetry.
��
��
The slope of g  x  is 2 so the line is steeper
than f  x  which has a slope of 1. The
y-intercept of g  x  is 3 so it is also translated
down 3 units after it has been rotated.
The new function is h  x   4x. The slopes
of g  x  and h  x  are opposites.
Each function below is reflected across the y-axis. Write a
function h  x  to describe each new graph.
5. f  x   5x
6. f  x   9x
7. f  x   2x  7
Describe the transformations from the graph of f  x  to the
graph of g  x .
8. f  x   x, g  x   4x  2
9. f  x   x, g  x   0.25x  3
10. f  x   2x, g  x   x  8
11. f  x   5x , g  x   x
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c05-9_rt.indd 71
71
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