In this lesson, students combine horizontal and vertical translations at the same time. Students analyze a set of graphs as they use function notation to describe one graph as a transformation of another.

They continue analyzing a context from a previous lesson to address the common misconception that subtracting from the input will result in a translation to the left. Next, students apply this understanding to a new context, where they compare multiple ways to translate a curve to fit data. By deciding which transformation of a function best fits a data set, students are building skills that will help them in mathematical modeling (MP4).