Lesson Title: Domain and Range Course: Common Core Algebra II Date: Teacher(s): Start/end times:

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1 Lesson Title: Domain and Range Course: Common Core Algebra II Date: Teacher(s): Start/end times: Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical Practices do you expect students to engage in during the lesson? Interpret functions that arise in applications in terms of a context. F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Interpret functions that arise in applications in terms of a context. F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. MP3: Construct viable arguments and critique the reasoning of others. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning. Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson? 1. In Algebra I, you learned about domain and range. Brainstorm with a partner everything you remember about domain and range. Include sketches or examples if that helps you show your knowledge. 2. Using the graph below, state the domain and range of the function. Lesson Closure Notes: Exactly what summary activity, questions, and discussion will close the lesson and connect big ideas? List the questions. Provide a foreshadowing of tomorrow. There are many different characteristics of functions that you will be learning about. At the start of next class, we will discuss the results of your exit ticket then focus on asymptotes and continuity. (See Domain and Range Warm Up and Exit Ticket) Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices. 1. After students discuss the warm up with a group, discuss their findings as a class. Explain that during this class we will continue to build on their ability to recognize the domain and range. 2. Assign students to pairs. Distribute Domain and Range Practice. Have students review Examples 1 and 2 and summarize understanding to partner. Have students work in pairs to find domain and range of the practice problems. Have pairs present solutions. (Look for evidence of MP3 and MP8.) 3. Distribute graph paper. Have pairs select a Domain and Range Grab bag sample problem. For each of the sample problems, the domain and range is provided. Have pairs create a sample graph that has the given domain and range. As a challenge, have pairs create a scenario that may have that given domain and range. As time allows, have students rotate grab bag items. (Note: Another option is to create stations with the grab bag items around the room.) 4. Students will complete the F.IF.4 Domain and Range Exit Ticket. Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.

2 Lesson Title: Domain and Range Course: Common Core Algebra II Date: Teacher(s): Start/end times: measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding. Students should have a solid understanding of domain and range. Students should understand that the end behavior of a graph determines the domain and range. I will measure students success through the results of the whiteboard activity and the exit ticket. Also, the accuracy of answers provided on the homework assignment will be an indicator of student mastery. Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc. Students had prior work with domain and range in Algebra I. Use this lesson to continue to gauge students prior knowledge and anticipate concepts that need to be reviewed. Resources: What materials or resources are essential for students to successfully complete the lesson tasks or activities? Domain and Range Practice Domain and Range Warm Up and Exit Ticket Grab Bag items Graph paper Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson? For homework, assign problems from the textbook which require students to identify the domain and range. Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson? Were students able to recall information on functions from Algebra I? Were students able to accurately recognize the domain and range of various functions? Were students able to accurately complete the exit ticket? Were students able to support their reasoning for why they chose the domain and range? Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.

3 Domain and Range Warm Up 1. In Algebra I, you learned about domain and range. Brainstorm with a partner everything you remember about domain and range. Include sketches or examples if that helps you show your knowledge. 2. Using the graph below, state the domain and range of the function. Domain and Range Exit Ticket 1. The graph below shows the number of items sold (x-axis) and the profit (y-axis). On what domain does the company have a positive profit? What do negative x-values represent? What do positive y-values represent? 2. What did you find most challenging about domain and range today? 3. How did you overcome the challenges that you encountered?

4 Sample A: Create a graph with - x 1 y Sample B: Create a graph with - x - y 4 Sample C: Create a graph with 0 x 0 y 10 Sample D: Create a graph with 0 x 15-3 y 5 Sample E: Create a graph with -3 x 2, 2<x 5 2 y 8 Sample F: Create a graph with 0 x 0 y

5 Sample G: Create a graph with - x 1 y Sample H: Create a graph with - x - y 0, 0 y Sample I: Create a graph with - < x 0 - < y 0 Sample J: Create a graph with - x -2 y 2 Sample K: Create a graph with -4 x 3 1< y 7 Sample L: Create a graph with - x -4 y 6

6 Domain and Range Specifying Domain and Range Describing the domain and range of a function is a common task and an important part of mathematical vocabulary. As you study various functions and examine various graphs and their symbolic representations you will be expected to give the domain and range. In this lesson you will practice several ways of stating a domain or range. In this graph the x values are from 2 to 8. The open circle at 8 indicates that this point is not included in the domain. The y values, or range, consist of the values between 1.5 and 6. Note that 1.5 is included in the range, but 6 is not. See how these values are indicated using each of the three methods in the chart below. Method Domain Range Description All real numbers between 2 and 8, including 2 All real number between 1.5 and 6, including 1.5 Inequality Signs 2 x y 6 Interval Notation [ 2, 8 ) [ 1.5, 6 )

7 Example 1 Infinity The infinity symbol is helpful when the domain or range continues forever in the positive direction. Method Domain Range Description All real numbers greater than -4 All real number greater than -5 Inequality Signs 4 x 5 y Interval Notation (-4, ) (-5, ) Example 2 Double Infinity Method Domain Range Description All real numbers All real numbers equal to or greater than 3 and less than or equal to 1 Inequality Signs - x 3 y 1 Interval Notation (-, ) [-3, ]

8 Practice Exercises For each relation state the domain and range using appropriate notation, and indicate whether the graph is a function

Algebra I Notes Relations and Functions Unit 03a

Algebra I Notes Relations and Functions Unit 03a OBJECTIVES: F.IF.A.1 Understand the concept of a function and use function notation. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element