Mastering Functions: Graphs, Domain, Range, and Transformations

The Organic Chemistry Tutor

A comprehensive pre-calculus tutorial mastering the fundamental concepts of functions. This video serves as an extensive guide to understanding parent functions, graphing techniques, and the algebraic manipulation of functions required for higher-level mathematics. The video systematically breaks down three major areas of study: (1) The library of parent functions (linear, quadratic, cubic, square root, absolute value, rational, exponential, logarithmic, and trigonometric) with their respective domains, ranges, and graphical behaviors; (2) Function transformations, detailing how to shift, reflect, and stretch graphs without plotting points; and (3) Advanced function operations including composite functions and finding inverse functions algebraically and graphically. This resource is an invaluable tool for the classroom as it bridges the gap between Algebra II and Calculus. Teachers can use specific segments to introduce individual function families, demonstrates the visual "scanning" method for finding domain and range, or provide step-by-step procedures for algebraic proofs of inverse functions. The clear, visual approach to graph transformations helps students build intuition rather than relying solely on memorization.