2.3 Functions and Relations
Miller & Gerken, College Algebra 2e — Pages 222-239
Learning Objectives
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Determine if a relation is a function
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Apply the vertical line test
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Find domain and range
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Use function notation
Key Concepts
Function Definition
A function is a relation where each input has exactly one output.
Vertical Line Test
A graph represents a function if no vertical line intersects it more than once.
Function Notation
\[f(x) = \text{expression in } x\]
\(f(a)\) means "evaluate the function at \(x = a\)"
Domain and Range
- Domain
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All valid input values (\(x\))
- Range
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All possible output values (\(y\) or \(f(x)\))
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