2.7 Analyzing Graphs of Functions
Miller & Gerken, College Algebra 2e — Pages 284-297
Learning Objectives
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Determine if a function is even, odd, or neither
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Identify intervals where a function is increasing or decreasing
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Find relative maxima and minima
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Analyze piecewise-defined functions
Key Concepts
Even and Odd Functions
- Even (symmetric about y-axis)
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\(f(-x) = f(x)\)
- Odd (symmetric about origin)
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\(f(-x) = -f(x)\)
Increasing and Decreasing
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Increasing on \((a, b)\): \(f(x_1) < f(x_2)\) when \(x_1 < x_2\)
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Decreasing on \((a, b)\): \(f(x_1) > f(x_2)\) when \(x_1 < x_2\)
Relative Extrema
- Relative Maximum
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Highest point in a local neighborhood
- Relative Minimum
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Lowest point in a local neighborhood
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