The purpose of this lesson is to introduce students to one of the big ideas of the unit: we can transform functions to model sets of data. The main focus of this lesson is to elicit ideas and language around transforming graphs that will be refined throughout the unit. Later in the unit, students will make connections between graphical and algebraic transformations and directly manipulate equations to transform graphs.
The two functions in Which Function? are both good fits for the data, providing students with the opportunity to make an argument about why a particular function is a better fit (MP3). Students continue to critique each other's arguments as they make adjustments to the functions to get a better fit. In the next activity students take turns describing transformations between pairs of graphs, giving an opportunity for students to refine their language and connect back to transformation vocabulary from geometry (MP6).
One of the activities in this lesson works best when each student has access to devices that can run the digital applet because students will benefit from seeing the graph in a dynamic way.
- Describe informally (orally and in writing) transformations of graphs.
- Describe (in writing) how to transform a given function to fit a data set.
- Let’s describe how to transform graphs.
Devices are required for the digital version of the activity, "Which Function?".
Be prepared to display data points and graphs using the embedded Desmos applet (recommended) or other graphing technology.
- I can describe how a graph is transformed.