In this lesson, students compare two functions, where one is a reflection of the other across an axis, using tables, graphs, and equations, making connections to their previous study of reflections in previous courses. They continue to work with function notation where one function is defined in terms of another.

Students begin by observing three graphs that show reflections across both the - and -axis. Students then study reflections across each of the axes individually, identifying what does and does not change for specific points on the graph being reflected. Students engage in repeated reasoning to notice patterns about the equations and graphs of functions that have been reflected across the - or -axis (MP8).

The work in this lesson builds directly into the two following lessons where students study even and odd functions, so there is no need to introduce these terms at this time.