Lesson 11

Examining Domains and Ranges

These materials, when encountered before Algebra 1, Unit 4, Lesson 11 support success in that lesson.

11.1: Notice and Wonder: A Wiggly Graph (10 minutes)

Warm-up

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.

Launch

Display the graph for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.

Student Facing

What do you notice? What do you wonder?

Student Response

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Activity Synthesis

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the graph. 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 the domain and range does not come up during the conversation, ask students to discuss this idea.

11.2: Moving Weeds and a Ball (15 minutes)

Activity

In this activity, students describe situations based on the graph 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.

Student Facing

1. Examine these graphs and describe a situation that could match the situation.
2. For each situation, give an example of a value that could be:
• In the domain
• Not in the domain
• In the range
• Not in the range

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

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. Ask students,

• “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)

11.3: Make It Realistic (20 minutes)

Activity

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.

Student Facing

1. What is wrong with these graphs?
1. The graph relates the length of a side for a square and the area of the square.

2. The graph relates the number of students going on a field trip and the cost of the trip.

3. The graph represents Han’s height since he was 4 years old until now when he is 14.

2. On each graph, draw a more realistic graph.

Student Response

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Activity Synthesis

The purpose of the discussion is to connect domain and range to realistic situations. Select students to share their solutions and explain why they think the graphs are wrong. 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.