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References: Introduction to Functions

  1. Function (mathematics) - Wikipedia - Comprehensive overview of the modern function concept, including formal definitions, notation, domain and codomain, and historical development. Provides the theoretical foundation for the chapter's core topic.

  2. Domain of a function - Wikipedia - Explains how the domain of a function is defined and restricted, with examples involving division and square roots. Directly supports the chapter's domain and range section.

  3. Piecewise function - Wikipedia - Describes how piecewise-defined functions are written and evaluated across different subdomains, including step and absolute value functions as special cases. Reinforces the chapter's discussion of piecewise and step functions.

  4. Algebra 1 (Common Core Edition) - Randall I. Charles et al. - Prentice Hall/Pearson - Chapter on functions covers relations, function notation, domain and range, and graphing with guided practice problems matching this chapter's scope.

  5. Big Ideas Math: Algebra 1 - Ron Larson and Laurie Boswell - Big Ideas Learning - Includes a dedicated functions chapter with function notation, evaluating functions, parent functions, transformations, and piecewise/step functions with worked examples.

  6. Introduction to functions - Purplemath - Explains the relationship between relations and functions, the vertical line test, and domain/range using clear, student-friendly language. Reinforces the chapter's opening distinction between relations and functions.

  7. What is a Function - Math is Fun - Introduces functions as input-output "machines," covering domain, range, and the requirement that each input maps to exactly one output. Supports the chapter's introductory explanation of functions.

  8. Domain, Range and Codomain - Math is Fun - Uses a vending-machine analogy to distinguish domain, codomain, and range, clarifying why these sets matter when defining a function. Deepens the chapter's domain and range coverage.

  9. Piecewise Functions - Math is Fun - Shows how to build and graph functions defined by different rules on different intervals, including jump discontinuities and the floor function. Directly supports the chapter's piecewise and step function sections.

  10. Function Transformations - Translations - Purplemath - Explains how adding or subtracting constants inside and outside a function shifts its graph up, down, left, or right. Supports the chapter's translation section, including the counterintuitive horizontal-shift rule.