The purpose of this Warm-up is to elicit the idea that the range of a function is not always all real numbers, which will be useful when students examine domain and range in a later activity. While students may notice and wonder many things about this graph, the domain and range are the important discussion points.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the graph. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

If the domain and range do not come up during the conversation, ask students to discuss this idea.

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).

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).