This worksheet starts but showing students the inner workings of a composition. This worksheet starts with the assumption that students have an understanding of transformations of functions. The first few questions have students understanding compositions and how they affect each other by visually analyzing. Questions are asked to induce thinking: like when is a composition commutative?, what does f of f mean? . Of course the sheet also practices the basics of using the operation and then finishes with some applications. Absolutely love the shopping questions. Produces a great deal of conversation. The final page is a practice student page.