The purpose of this Warm-up is to elicit the idea that graphs can be reflected both vertically and horizontally, which will be useful when students generate a table and graph for and from in a later activity. Students should be familiar with the properties of reflections from a previous course. While students may notice and wonder many things about these images, being precise about how the graphs are related is the important discussion point.

This prompt gives students opportunities to see and make use of structure (MP7). They should notice that the distance of each point on the graph to the line of reflection is the same but in a different direction after the graph is reflected. In this unit, reflections across the - and -axes are the focus.

Ask students to share the things they noticed and wondered. Record and display their responses. If possible, record the relevant reasoning on or near the graphs. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.

If lines of reflection do not come up during the conversation, ask students to discuss this idea. Students will focus on what values do and do not change when reflecting across the - and -axes during this lesson, so it is okay if students do not focus on specific coordinate values at this time.

In this activity, students compare two functions where one is a reflection of the other across the -axis. They first use coordinates on the graph of to complete a table and compute for each -value in the table. Students then plot on the same axes as , allowing them to directly compare the graphs of and  before explaining why   means the graph of is a reflection of the graph of  across the -axis.

In this activity, students compare two functions where one is a reflection of the other across the -axis. Students first use the coordinates on the graph of to complete a table and compute for corresponding points in the table. Students fill in both - and -coordinates for the function . They then plot on the same axes as  to compare the graphs directly before explaining why means the graph of is a reflection of the graph of across the -axis. As students build on thinking from a previous activity, they engage in repeated reasoning to make observations about graphs that are reflected across an axis (MP8).