How to Find the Domain of Radical Functions Algebraically

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on finding the domain of radical functions algebraically, without relying on graphing calculators. The narrator progresses from simple linear radicals to rational functions involving radicals, and finally to complex quadratic radicands. The video emphasizes the critical difference between radicals appearing in the numerator versus the denominator and how this affects inequality constraints. Key themes include solving linear and quadratic inequalities, using number lines (sign charts) to test intervals, and mastering interval notation. The tutorial also highlights the distinction between even-indexed roots (like square and fourth roots) which require domain restrictions, and odd-indexed roots (like cube roots) which are generally defined for all real numbers. This resource is highly valuable for Algebra II and Pre-Calculus classrooms as it bridges the gap between simple algebraic manipulation and the conceptual understanding of function validity. By visualizing solutions on number lines, it helps students grasp why certain intervals are included or excluded, solidifying their understanding of domain constraints before moving on to more advanced calculus concepts.