# The Great Domain

## Domain and Range Notations

Brittany VanCleave, Lindsey Link, Laura Halstied, Michell Eike, Samaya Williams, Laura Young, Lydia Baker | Published: August 19th, 2022 by K20 Center

• Grade Level 10th, 11th, 12th
• Subject Mathematics
• Course Algebra 2, Precalculus
• Time Frame 80-95 minutes
• Duration 2 class periods

### Summary

This lesson focuses on the notation for writing domain and range of a function. Students will recall their knowledge of domain and range then formalize their understanding of algebraic, set, and interval notation. This lesson is designed to be taught at the beginning of an Algebra II course. There are extension opportunities in this lesson for use in a precalculus course.

### Essential Question(s)

How can you represent and describe a function in relation to its domain and range?

### Snapshot

Engage

Students reflect on their knowledge of domain and range through the Always, Sometimes, or Never True strategy.

Explore

Students recall their knowledge of domain and range.

Explain

Students formalize their understanding of algebraic, interval, and set notation for domain and range.

Extend

Students apply their understanding to create graphs given different notations of the domain and range.

Evaluate

Students reflect on their learning by using the Muddiest Point strategy.

### Materials

• Lesson Slides (attached)

• Home on the Range handout (attached; one per student; printed front only)

• Guided Notes handout (attached; one per student; printed front only)

• Guided Notes (Model Notes) document (attached; for teacher use)

• Wrangle Up Domain and Range handout (attached; one per student; printed front only)

• Paper

• Pencil

### Engage

10 Minute(s)

Introduce the lesson using the attached Lesson Slides. Display slide 3 to show the lesson's essential question: "How can you represent and describe a function in relation to its domain and range?" Slide 4 identifies the lesson's learning objective. Review each of these with students to the extent you feel necessary.

Display slide 5 and introduce the steps for the Always, Sometimes, or Never True instructional strategy. Show slide 6 to give students a pictorial definition for "bounded" and "unbounded." At this time, try not to give more than this as the definition, as students do not need more of a definition at this time. However, if students need additional clarification, a ray would be considered "bounded."

Go to slide 7 and have students discuss with an elbow partner the first Always, Sometimes, or Never True statement: "Domains are y-values and bounded by the graph." Give the pairs one minute to analyze the statement and choose their claim. After one minute, display the next statement on slide 8 and repeat the process. Once each statement has been shown and the students had time to state their claim, have a whole group discussion about the statements by letting different pairs share their viewpoints on the topic.

This particular strategy can have various justifications, some justifications that students provide can support the incorrect answer. Focus on justifications for this activity. Use student responses to determine what misconceptions need to be addressed during the Explain portion of the lesson.

### Explore

20 Minute(s)

Go to slide 10 and give each student a copy of the Home on the Range handout. Introduce students to the I Think / We Think strategy. Have students individually find the domain and range for each of the given graphs. Guide them to write their answers in the "I Think" column. This is the time for students to express what they know and don't know about domain and range.

After a few minutes, put students into groups of 3–5. Direct groups to discuss their reasonings to come to a group conclusion for the domain and range of each graph. Instruct students to all record what their group decided into the "We Think" column.

Facilitate a whole class discussion over the graphs. Ask for volunteers to share what their group found for domain and range on the first graph. Repeat this with different volunteers for each graph. Use student responses to determine if students need a quick review of finding domain and range before moving to the next portion of the lesson.

### Explain

20 Minute(s)

Go to slide 11 and give each student a copy of the attached Guided Notes handout. Complete handout as a class.

Once finished, have students add this to their math notebook if that is a classroom norm.

### Extend

25 Minute(s)

Show slide 15. Pass out the attached Wrangle Up Domain and Range handout to each student. Have students try questions 1-2 on their own.

After students finish question 2, display slide 16 and have them find a partner or assign partners to share their created graphs. Transition through slides 17–18 so that students can compare their graphs with the sample responses on the slides. Bring the class together for a whole-class discussion asking the class what is the same and different about their graphs with the sample responses on the slides. Consider using the following questions to facilitate a class discussion.

• What is important to consider about the domain?

• What is important to consider about the range?

Show slide 19 and instruct students to work with their partner to create a graph for question 3. As students finish question 3, show slide 20 for students to compare their graphs with the sample responses. Then show slide 21 and bring the class together for discussion.

• What is important to consider about the domain?

• What is important to consider about the range?

• What did you find easy about creating this graph?

• What did you find difficult about creating this graph?

### Evaluate

5 Minute(s)

Go to slide 22. Have students reflect on the lesson and their overall understanding of the content using the Muddiest Point strategy. Have students answer the following questions:

• Crystal Clear: What do you think is the easiest part of writing domains and ranges using different notations?

• Muddiest Point: What do you think is the most confusing part of writing domains and ranges using different notations?

You can collect responses in a variety of ways depending on your class. Sticky notes, pieces of paper, or digital posts are a few examples.