How to Evaluate Piecewise Functions

Miacademy & MiaPrep Learning Channel

This educational video provides a clear, step-by-step tutorial on how to evaluate piecewise functions. Moving beyond simple step functions, the narrator explains how to handle functions defined by different algebraic expressions over specific domain intervals. The video covers identifying the correct interval for a given input, handling boundary values where inequalities utilize "less than or equal to," and performing the final substitution to find the output. The content progresses from two-part functions defined by inequalities to more complex three-part functions. A significant portion of the video is dedicated to explaining interval notation (using brackets and parentheses), translating it from standard inequality notation, and applying it to evaluation problems. This dual focus ensures students are comfortable seeing domain restrictions written in multiple standard mathematical formats. This resource is highly valuable for Algebra I and Algebra II classrooms. It demystifies the intimidating appearance of piecewise functions by breaking the process down into a simple decision-making tree: check the input against the domains, select the rule, and evaluate. The inclusion of a "pause and solve" practice problem at the end allows for immediate formative assessment, making it a perfect tool for flipped classrooms or direct instruction reinforcement.