# Domain and Range

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## Objective

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

#### Big Idea

Students will use real world examples to solidify their understanding of continuous and discrete inputs and outputs.

## Do-Now

10 minutes

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."

## Whole Group Discussion + Practice

40 minutes

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 OneDay Two.

## Partner Practice: Versatiles

20 minutes

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.

## Closing

10 minutes

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.