The purpose of this Warm-up is for students to recall some of the ways functions can be represented, such as tables, graphs, equations, and descriptions. The focus here is on exponential and linear functions, and identifying the rates of change and growth factors.

The purpose of this discussion is to make sure students understand how to identify the growth factor or rate of change of sequences represented in different ways.

Display the questions for all to see throughout the discussion. For each problem, select students to share how they identified either the growth factor or rate of change. Highlight any comments linking these sequences to linear or exponential functions, such as that the rate of change would be the slope of the line that the terms of the sequence are on when graphed.

In this partner activity, students take turns matching a sequence to a definition. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).

One sequence and one definition do not have matches. Students are tasked with writing the corresponding match.

Monitor for students using clear reasoning as they create a recursive definition for the sequence 18, 20, 22, 24 to share during the discussion.

Making a spreadsheet available gives students an opportunity to choose appropriate tools strategically (MP5).

The purpose of this task is for students to write a recursive definition for a sequence that represents a mathematical context and to create other representations of the sequence.

Monitor for groups who create their recursive definitions in different ways to share during the whole-class discussion. For example, some students may first create a table showing step number and the associated values, while others may draw additional steps.

Allow students to use graph paper to sketch their graphs if needed. Making graphing technology available gives students an opportunity to choose appropriate tools strategically (MP5).