In this activity, students describe situations based on the graph and then identify examples of values that are in the domain and range or not. In the associated Algebra 1 lesson, students describe the domain and range of functions from graphs. Students are supported with this activity by focusing on single values rather than describing the entire domain and range. Students reason abstractly and quantitatively by explaining the context of graphs (MP2).

The purpose of the discussion is to think about different kinds of things that could be in the domain and range of a function. Select students to share their descriptions and values that are in or out of the domain and range. After each response is shared, ask if students have other examples. For each value shared, display it for all to see. Here are some questions for discussion:

• “For each graph, is there a good way to describe the numbers that are in the domain? What about the numbers that are in the range?” (It is not essential that students answer this clearly at this point. They will get more information in the Algebra 1 lesson associated with this support lesson.)
• “When thinking about values that might be in the domain and range, it can help to think about different kinds of numbers that might be possible. What are some types of numbers that might be useful to think about?” (Very large numbers like 1 trillion, zero, fractional values between whole numbers like 1.3, negative numbers like -8, very small numbers near zero like 1 trillionth)

In this activity, students examine graphs of functions representing situations and criticize what is wrong with the graphs. In the examples provided, there are issues with the domain and range of the graphs. Students are then asked to draw more realistic graphs for the described situations. As students redefine the domain and range to make the graphs more realistic they model with mathematics (MP4).

The purpose of the discussion is to connect domain and range to realistic situations.

Direct students’ attention to the reference created using Collect and Display. Ask students to share what is wrong about the graphs and why they think they are wrong. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

If possible, display the realistic graphs for all to see. Ask students if they agree that the solutions drawn are more realistic and whether they might be improved further.