2.6 Transformations of Graphs
Miller & Gerken, College Algebra 2e — Pages 268-283
Learning Objectives
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Apply vertical and horizontal shifts
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Apply reflections across axes
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Apply vertical and horizontal stretches/compressions
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Combine multiple transformations
Key Concepts
Vertical Transformations
| Transformation | Effect |
|---|---|
\(f(x) + k\) |
Shift up \(k\) units |
\(f(x) - k\) |
Shift down \(k\) units |
\(a \cdot f(x)\) (\(a > 1\)) |
Vertical stretch |
\(a \cdot f(x)\) (\(0 < a < 1\)) |
Vertical compression |
\(-f(x)\) |
Reflect across x-axis |
Horizontal Transformations
| Transformation | Effect |
|---|---|
\(f(x - h)\) |
Shift right \(h\) units |
\(f(x + h)\) |
Shift left \(h\) units |
\(f(-x)\) |
Reflect across y-axis |
Examples
Example 1. Example 1
Work through textbook example…
Practice Problems
Problem 1 (p. XX, #YY)
Problem:
My Work:
Answer:
Section Summary
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Key point 1
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Key point 2