Here are images from a handout that serves as an introduction to piecewise functions. The focus is to develop conceptual understanding of piecewise before attempting to graph independently. The work is divided into chunks to reduce the level of task demand at a given time in the process.
The first section has an application and introduces the idea of pieces addressed together. The graph is discrete which allows the students to see the points in lieu of looking at lines.
Pages 2 and 3 provide scaffolding for graphing. Page 2 presents the sections separately. Page 3 pulls them together, but with the intervals physically separated into columns over the graph.
Finally, the students are introduced to the function notation, with additional scaffolding. They are also asked to identify y-values for given x-values in function notation to help connect x-values with different pieces.