The goal of this lesson is to apply transformations to different functions in order to model a set of data. Students examine the key function types that they have studied up to this point: polynomials, rationals, radicals, and exponentials. In each case, once the basic shape of the function type is chosen, vertical and horizontal translations, scalings, and reflections are applied in order to model the data as well as possible. Since each function type can be made to fit the data well, context also plays an important role in choosing the best model.

Students model temperature data with different functions. They consider how well each model fits the data and the behavior of each model as time continues to elapse. Students use the shape of the function and the structure of each translation or scaling in order to find an appropriate combination (MP4).

While the data is given, only a partial model (the general function type) is included, and students need to build an accurate model from here by applying transformations. This can be done by hand via experimenting, but students may also choose to use graphing technology to help choose the appropriate translations, scalings, and reflections (MP5).