Determining Polynomial End Behavior and Limits

Miacademy & MiaPrep Learning Channel

This video provides a comprehensive guide to understanding and determining the end behavior of polynomial functions. It breaks down the concept into four distinct types of behaviors based on the visual direction of the graph's "tails" (e.g., "Start low, end high"). The narrator, Randy, explains how to predict these behaviors by analyzing the equation's degree (even or odd) and the sign of its leading coefficient (positive or negative). The video introduces formal mathematical notation for limits (as x approaches infinity) alongside plain English descriptions, making abstract concepts accessible. It uses a structured table to organize the four cases, providing example graphs and equations for each scenario. The lesson concludes with a set of practice problems where viewers apply the rules they've learned to match equations with their corresponding graph behaviors. Teachers can use this video to bridge the gap between algebraic expressions and their graphical representations. It is particularly useful for introducing the Leading Coefficient Test in Algebra 2 or Pre-Calculus. The visual breakdown helps demystify limit notation, and the clear rules provide students with a reliable method for sketching or identifying polynomial graphs without needing to plot multiple points.