If students are not sure how to start writing a function, consider asking:

• “What do you know about the function?”

• “How could a table of values help you write the function? For example, what is the height when is or ?”

Display the graphs of all three functions, , , and on the same coordinate plane, and ask students to identify which is which and to explain how they know.

If students do not use the term "vertical stretch" (or equivalent) to describe the difference between the graphs, do so now, calling back to their work in an earlier unit. Tell them that for these types of functions, the parameter, , in the equations and changes the “height” of each graph by a factor of and that the absolute value is called the amplitude. Highlight where to find the amplitude in the equations for the blades of length 3 meters and 0.5 meters.

If students are not yet sure how to start writing a function, consider asking:

• “How is this windmill similar to and different from the one in the previous activity?”

• “How could a table of values help you write the function for this new windmill? For example, what is the height when is , , , or ?”

The purpose of this discussion is to introduce students to the term "midline." This is also an opportunity to check and make sure students understand that periodic functions transform just like the other types of functions they have studied previously.

Begin the conversation by asking students to describe how the graph  compares to the graph of . Highlight that the shape is identical but it is translated upward by 8 units. If not mentioned by students, remind them that this is called a vertical translation. Contrast this type of transformation with the difference between the graphs of and : While these have the same general wavelike shape one is not a translation of the other. The coefficient of 3 "stretches” the shape vertically, making the graph steeper as it goes between the larger maximum values and smaller minimum values.

Conclude the discussion by displaying the graph of  . Ask, “What value would you say is the 'middle' value for the outputs of this function?” After a brief quiet think time, invite students to share their thinking. The important takeaway here is that is the "visual center" of the graph and is called the midline. For practice, ask students to consider the equation  . Its graph has a midline of  because its -values are centered around -3. A negative midline means that the graph is translated downward rather than upward.