How to Graph and Transform Absolute Value Functions

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step introduction to absolute value functions and their graphs. It begins by defining absolute value conceptually as a measure of distance from zero, explaining why outputs are always non-negative. The narrator then demonstrates how to graph the parent function f(x) = |x| by plotting points to reveal the characteristic "V" shape and defining the vertex. The core of the lesson focuses on transformations, specifically translations using the vertex form f(x) = a|x-h| + k. The video visually demonstrates how the variable 'k' shifts the graph vertically and how 'h' shifts it horizontally. Special attention is given to the counter-intuitive nature of horizontal shifts, explaining why a positive sign in the equation results in a leftward shift and vice versa. This resource is highly valuable for Algebra students encountering function transformations for the first time. It addresses the common student misconception regarding sign changes in horizontal shifts and provides a logical framework for graphing equations without needing to create a table of values for every problem. The visual animations effectively link the algebraic equation to the geometric position of the graph.