This lesson continues to look at how adding a constant or multiplying by a constant can transform the graphs of and to match a situation. Students study the equations of functions representing a situation and interpret what the different parts of the equation tell us, reasoning abstractly and quantitatively (MP2). Whereas in the previous lesson students focused on the effect of a single transformation, here they consider changes to both the amplitude and midline in the same function.

Students then consider horizontal translations of cosine and sine functions. In particular, they examine the graph of for a specific value of determined by a context. In the next lesson, students will work with these three types of transformations at once.

In this lesson, students also encounter the graph of a sine function that has a negative coefficient, making sense of it in the context of a windmill blade rotating clockwise.

Students also consider the structure of transformations of functions when they study the function  (MP7). Through the table of values and the context, they can identify that this is a cosine graph that has been translated horizontally.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.