The purpose of this activity is to build on the work of the Warm-up as students determine which of the given functions is a better fit for the data. For this activity, students should use any language that makes sense to them to describe why a function is or is not a good fit and how they would change the function to be a better fit for the data. Since both functions offer reasonably good fits for the data, students have the opportunity to make an argument about why they think a particular function is a better fit (MP3).

Monitor for students using different explanations of what makes a function fit the data, such as by focusing on the general shape of the graph, the accuracy of individual points, or the average error for all the points.

In the digital version of the activity, students use an applet to check their initial response to the question about which function better fits the shape of the data. The applet allows students to zoom out on the graph and see the part of the rational function that is not visible in the initial graphing window.

This activity works best when each student has access to devices that can run the Desmos applet because students will benefit from seeing the relationship in a dynamic way. If students don't have individual access, projecting the applet will be helpful during the Activity Synthesis.

In this partner activity, students take turns describing transformations of a graph and sketching the transformed graph from the description. As students trade roles explaining their thinking and listening, they have opportunities to refine and use more precise language when describing transformations (MP6).

Students may describe the transformations without enough detail, making it difficult for their partner to sketch the correct transformation. If this happens, consider saying:

• “Tell me more about what features of the graph stand out to you.”

• “What are two different ways you could describe those features to help your partner make their sketch?”

The purpose of this discussion is for students to describe the transformations they saw when graphing. Direct students’ attention to the reference created using Collect and Display. Ask students to share what types of transformations they saw. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases. Students will continue to refine their language around graphical transformations throughout the unit, so it is okay for students to use more informal language at this time.

As students share, display the graphs to help illustrate student descriptions, and connecting back to the list of words recorded during the activity. Connect any words students used to geometry vocabulary (“translate” and “reflect”). Ask, “Are any of these transformations dilations?” (No, they are stretching in only one direction.)

In order to show the temperature trend better, the first tick mark on the temperature axis represents 45 degrees, even though each successive tick mark represents only an additional 5 degrees. If students are confused that the first tick mark does not represent 5 degrees, remind them that since the range of this function does not include any numbers less than 45, it is convenient to start the range values at 45.