Domain and Range - Your Definitive Guide for Algebra 1 to Precalculus

Learn a systematic approach to finding domain and range of functions through a comprehensive 27-minute video tutorial that transforms confusing concepts into a clear, repeatable process. Start with the intuitive "vending-machine" analogy to understand inputs and outputs, then master the visual "flashlight trick" for reading domain and range directly from graphs. Build your algebraic toolkit by identifying three critical "red flags": denominators that cannot equal zero, radicands that must be non-negative, and logarithm arguments that must be positive. Progress through increasingly complex scenarios including piecewise functions, composite functions, and cases with multiple restrictions. Discover techniques for finding range algebraically without relying on graphs, and tackle advanced challenges like radicals in denominators that require strictly positive values. The tutorial provides a unified workflow applicable across Algebra 1, Algebra 2, and Precalculus levels, complete with timestamped sections for easy navigation and practical takeaways to reinforce key concepts.