Define Piecewise Function Notation

The video tutorial introduces piecewise functions, starting with a warmup on graphing functions with domain restrictions. It covers graphing functions with specific domain restrictions and transformations, including reflections and horizontal shifts. The tutorial explains how to define and combine piecewise functions, ensuring they pass the vertical line test. Key concepts include understanding domain restrictions, transformations, and the structure of piecewise functions.

Discuss the significance of including or excluding endpoints in a piecewise function.

How can you combine multiple functions into a single piecewise function?

Explain how to graph the function Y = -X^2 - 1 with the restriction X ≤ 0.

What is the role of transformations in understanding the behavior of piecewise functions?