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Chapters

This textbook is organized into 13 chapters covering 208 concepts.

Chapter Overview

  1. Algebra Foundations - Introduces variables, constants, expressions, equations, inequalities, number systems, and core algebraic manipulation techniques.
  2. Relations and Functions - Establishes the concept of relations and functions, domain, range, function notation, and the coordinate plane.
  3. Graphing and Key Features - Covers graphing functions, intercepts, slope, turning points, concavity, and effective use of graphing technology.
  4. Linear Functions - Explores gradient forms of lines, parallel and perpendicular lines, simultaneous equations, and linear modeling.
  5. Quadratic Functions - Covers parabolas, three quadratic forms, the discriminant, solving techniques, and quadratic applications.
  6. Inverse and Composite Functions - Introduces one-to-one functions, inverses, the reciprocal function, and composite functions.
  7. Exponential Functions - Covers exponential growth and decay, Euler's number, and real-world exponential models.
  8. Logarithmic Functions - Explores logarithms as inverses of exponentials, logarithm laws, and solving log equations.
  9. Polynomial Functions - Investigates higher-degree polynomials, factor and remainder theorems, and root properties.
  10. Rational Functions - Analyzes asymptotes, rational function forms, and graphing rational functions.
  11. Function Classifications - Classifies functions by symmetry, periodicity, modulus operations, and piecewise definitions.
  12. Transformations - Covers translations, reflections, stretches, and composite transformations.
  13. Modeling and Applications - Applies functions to real-world scenarios through regression, curve fitting, and the modeling cycle.

How to Use This Textbook

Chapters are sequenced so that each chapter builds on concepts from earlier chapters. Complete the chapters in order for the best learning experience, as the dependency structure ensures you always have the prerequisite knowledge before encountering new material. Chapters 1-3 establish essential foundations, Chapters 4-10 cover the major function families, and Chapters 11-13 explore advanced classifications, transformations, and applications.

Note: Each chapter includes a list of concepts covered. Make sure to complete prerequisites before moving to advanced chapters.