The purpose of this lesson is for students to start from an expression of a familiar function and write expressions for the transformation of the function from descriptions of the graphical transformation. These transformations include translations and reflections, and require students to focus on what each part of the expression tells them about the corresponding graph (MP7). 

The Information Gap structure encourages students to think carefully about the order in which individual transformations are applied. They also need to communicate precisely how applying a scale factor to the input or output affects the graph of the function (MP6).

There is an optional activity that gives students an opportunity to make connections between transforming a function and the vertex form of a quadratic equation.