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# Domain and Range

Lesson 2 of 10

## Objective: SWBAT identify the domain and range of a function. SWBAT analyze the domain and range of continuous and discrete functions.

#### Do-Now

*10 min*

Students will complete today's Do Now. These problems review operations with integers, giving my students the opportunity to maintain or continue to develop fluency (**MP6**). While students are working, I will circulate around the room passing back the graded Exit Cards from our last class.

After about 4 minutes, I will call the problems from the Do-Now aloud, and students will echo back the answer. Then, we will quickly discuss the responses to the yesterday's Exit Cards.

Next a student volunteer will read today's lesson objective, ** "SWBAT identify the domain and range of a function. SWBAT analyze the domain and range of continuous and discrete functions."**

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For the majority of my students **domain** and **range** are new concepts. To introduce this topic to them I will use the chart on **Slide 3** of Domain and Range. I begin by asking five or six volunteers to tell me their name and their birth date. I continue asking for volunteers until I get two students with the same birth month. To reinforce what we learned yesterday about Functions, I will then ask students to decide if the relation, name and birth month, is a function.

Next, I will ask a student to read **Slide 4** aloud. Then, I will allow students to come up with their own definition of domain. I will list the domain of the Name/Birthday example as:

{Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec}

I stress the word "possible" in the definition of domain. I will ask students to briefly brainstorm with a partner why this word is important in the definition.

On **Slide 8** I will call on additional student volunteers to supply their birthday and their names. Again, I will ask the class to decide if this is a function. A student will read **Slide 9** aloud, and we will discuss as a group the definition of the range of a function.

**Domain:** {1, 2, 3, ... 29, 30, 31}

**Range:** {Students names in the class}

To continue the discussion of "possible input values" from the definition, I will ask students to state the domain of our example on Slide 8, and justify if the number 32 is in our domain.

**Slide 11:** Next we will talk about what it means for a function to be continuous or discrete. I will ask students to examine the word "continuous" to find the hidden word (continue). I will tell students that a continuous function is a function where the input values include all possible values within a parameter. I will guide students to examine the domain values first to determine whether a function is continuous or discrete.

**Teaching Note:**

The concept of "infinity" and what it means for a line to to extend endlessly in a direction is often brand new for my students. This idea requires them to think abstractly, and view a coordinate plane as an infinite plane that has no ending, not just the 10x10 box that is commonly seen on a paper. This misconception is typically evident when I ask students to identify the domain and range of the line y=x, and they describe the domain using the numerical window constraints.

To help students visualize that a linear function will go on forever, I will project this site on my board. (To make the graph easier to view as a whole group, I use the settings to place the graph in "projector mode" as well as zooming in the screen using my browser settings). I plan to graph a variety of functions and zoom out many times to show students that the line never "stops" making the domain and range all real numbers. I will frequently use this resource throughout the year to reinforce this idea with multiple standards.

**2015 Update:** This lesson felt like something was missing. I have now created two sets of guided notes to be used over two days to support students as they learn this concept: Day One, Day Two.

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#### Partner Practice: Versatiles

*20 min*

Students will work in pairs to practice finding the domain and range of a function using the Domain and Range Versatiles handout. Students will match each question to the box on page two that corresponds to its correct response.

To assist those who are still struggling with the domain and range of a continuous function, I will pass out colored pencils and tell students to shade the x and y axis with a different color below the function on the graph.

#### Resources

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#### Closing

*10 min*

To bring this lesson to closure, we will have a brief summary discussion. I will ask students to explain the definition of domain and range in their own words, and, to give an example of a situation that would have constraints or a situation where all of the input values are not possible. I will also ask the class to elaborate on their understanding of continuous and discrete functions.

Students will then complete an Exit Card for today's lesson.

#### Resources

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*This is an exceptional lesson. I think my students will thoroughly enjoy discussing the slide on determine whether the situation is discrete or continuous. It reinforces the concept I've already introduced. Thanks for posting your lessons. | 7 days ago | Reply*

I think this is an excellent lesson. I had difficulty downloading one of the resources onto my laptop because it deleted the graphs, table, and diagram when I opened it on my computer. Nevertheless, I loved the multiple representations students have to analyze to determine the domain and range. I shared the idea with our math teachers and gave them a few suggestions. We talked about making it into more of a card sort and having students paste on the correct answers. We also discussed extending the activity by having students determine whether or not each relation is a function or not a function. This is a wonderful lesson. It generated some good ideas. Thank you for sharing.

| 2 years ago | Reply##### Similar Lessons

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- UNIT 1: Welcome Back! - The First Week of School
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- LESSON 1: What is a Function?
- LESSON 2: Domain and Range
- LESSON 3: Function Notation
- LESSON 4: Writing Linear Equations (Day 1 of 2)
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