Graph Transformations: Shifts, Scaling, and Reflections

Understanding how algebraic changes in a formula affect the visual representation of a function is an essential math skill. This written course guides you step by step through the core mechanics of function transformations, helping you build a clear mental model for high school math, standardized exams, and university calculus. You will begin with basic terminology, function notation, domain, range, and standard parent functions. From there, you will systematically study how modifying formula parameters alters graph positions and shapes. What you will learn: Learn key mathematical terminology, function notation, and characteristics of standard parent functions. Apply horizontal and vertical translations to shift function graphs precisely across coordinate axes. Understand horizontal and vertical stretching and compression. Master reflections across the coordinate axes and analyze absolute value transformations. Practice breaking down complex, multi-step transformations through detailed written examples. Explore modern applications of function modeling and piecewise defined functions. The course begins with clear foundational concepts before advancing through structured algebraic rules and written analysis exercises. Perfect for high school students, incoming college freshmen, and self-learners, this course requires only basic introductory algebra. Start reading today to sharpen your mathematical graphing skills.