How to Shift Functions Horizontally and Vertically

Miacademy & MiaPrep Learning Channel

This video provides a clear and concise tutorial on how to transform mathematical functions through horizontal and vertical shifts. Hosted by an instructor named Randy, the lesson breaks down the general transformation formula $g(x) = (x-h)^a + k$, distinguishing between the "core function" (parent function) and the transformation parameters. The video specifically focuses on polynomial functions where the exponent is a positive integer, making it accessible for Algebra students encountering function families for the first time. The central theme of the video is distinguishing between "intuitive" vertical shifts and "counter-intuitive" horizontal shifts. Through visual aids and annotated formulas, the instructor explains that while adding a constant ($k$) to the end of a function moves it up or down as expected, adding or subtracting a constant inside the function's parentheses ($h$) moves the graph in the opposite direction of the sign. This mnemonic of "intuitive vs. not intuitive" serves as a primary memory aid throughout the lesson to help students avoid common sign errors. For the classroom, this video serves as an excellent instructional bridge between basic graphing and more complex function transformations. It includes three distinct worked examples: interpreting a visual graph of parabolas, translating a written description of a cubic function shift into an equation, and writing an equation for a quartic function based on specific directional movements. Teachers can use this resource to introduce the vertex form of quadratics or to reinforce the universal rules of transformations that apply across all function families.