2.6 Transformations 2011
September 19, 2011
2.6 ­ Graphing Techniques: Transformations
Objective: Apply transformations to functions and their graphs.
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
How does changing certain aspects of a function affect its graph?
Vertical shift:
y = f(x) + k
k > 0 shifts up
k < 0 shifts down
Identify the parent function.
Write the function to match the graph.
Oct 22­1:54 PM
2
2.6 Transformations 2011
September 19, 2011
How does changing certain aspects of a function affect its graph?
Horizontal shift: y = f(x ­ h)
h > 0 shifts right
h < 0 shifts left
Identify the parent function.
Write the function to match the graph.
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
How does changing certain aspects of a function affect its graph?
Vertical stretch or compression:
y = af(x)
a > 1 vertical stretch
0 < a < 1 vertical compression
Identify the parent function.
Write the function to match the graph.
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
How does changing certain aspects of a function affect its graph?
reflection about the x­axis: y = ­ f(x)
Identify the parent function.
Write the function to match the graph.
Oct 22­1:54 PM
5
2.6 Transformations 2011
September 19, 2011
How does changing certain aspects of a function affect its graph?
reflection about the y­axis: y = f(­x)
Identify the parent function.
Write the function to match the graph.
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
Determine the function obtained from a series of transformations.
f(x) = x 2
1. shifted right 4 units
2. shifted up 3 units
3. reflected about the y­axis
2
f(x) = (­x ­ 4) + 3
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
Determine the function obtained from a series of transformations.
f(x) = |x|
1. shifted left 5 units
2. vertical stretch of 2
3. reflected about the x­axis
f(x) = ­2|x + 5|
Oct 22­1:54 PM
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2.6 Transformations 2011
September 19, 2011
ING GRAPHS
Oct 23­11:20 AM
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2.6 Transformations 2011
September 19, 2011
Autobots, graph f(x) = 3|­x + 2| ­ 1
Hint: It may be easier to graph in stages.
Oct 23­11:20 AM
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2.6 Transformations 2011
September 19, 2011
Only the graph of 3
f(x) = ­(x + 2) ­ 3
can stop me now!!!
Oct 23­11:20 AM
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2.6 Transformations 2011
September 19, 2011
2
f(x) = ­x + 3?
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2.6 Transformations 2011
September 19, 2011
There's more then meets the eye with these functions!
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2.6 Transformations 2011
September 19, 2011
Homework: page 128 (41 ­ 61) odd
*Label at least 3 points on each graph! (due Wed)
Project: Complete picture graphs and functions. Check on a graphing calculator. (due Friday)
Oct 23­11:20 AM
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