How to Graph Piecewise Functions Step-by-Step

Miacademy & MiaPrep Learning Channel

This instructional video provides a clear, step-by-step guide on how to graph piecewise functions. It begins by transitioning from algebraic evaluation to graphical representation, showing students how to graph individual linear equations and then apply domain restrictions to "cut" the graph to the correct shape. The video covers two main examples: a standard two-part linear function using inequality notation and a more complex multi-part function using interval notation. A key moment in the video connects piecewise functions to absolute value functions, demonstrating how an absolute value graph is essentially a specific type of piecewise function with two linear branches meeting at a vertex. This helps scaffold new knowledge onto concepts students likely already know. The tutorial emphasizes critical details such as determining whether endpoints should be open or closed circles based on the inequalities or interval brackets used. For educators, this video serves as an excellent direct instruction tool or review resource for Algebra units on functions. It visually demonstrates the concept of domain restrictions in a way that static textbook images cannot, specifically showing the process of graphing the "whole" line and then removing the irrelevant parts. The inclusion of a pause-and-practice problem at the end allows for immediate formative assessment of student understanding.