In a previous unit, students examined how each of the constants and influences the graph of for a given function . This unit has looked in depth at the special case of trigonometric functions. If , for example, then is the amplitude of  while  is a horizontal translation,  is a vertical translation, and the period of is . In this lesson, students examine these parameters and how they influence trigonometric functions and their graphs. This lesson also includes an optional activity using technology for extra practice transforming periodic functions.

The Information Gap structure encourages students to think carefully about the order in which individual transformations are applied. They also need to think carefully about signs for the translations and about the coefficient of in the transformed function to correctly identify how the graph is scaled horizontally. Students have had opportunities to observe the close relationship between transformations of graphs and transformations of functions in the lessons leading up to this one, and they now have a chance to describe these transformations with increasing precision (MP6).