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Compare the impact of different interest rates in situations about money to the function rules modeling those situations.

This Core Resource supports students in investigating, primarily using rate of change, how linear functions are different than exponential functions.

Students compare arithmetic and geometric sequences and connect these two linear and exponential functions respectively. Students then analyze situations to determine what function type, linear or exponential, best models the situation.  

What is not yet covered in this resource is representing piecewise, step, or absolute functions as graphs, calculating average rate of change, and writing explicit and recursive descriptions of functions.

Describe connections between how the rate of change and initial value are represented in a situation and its function rule. 

Students will use what they know about function transformations to connect function rules with tables of values.

The primary focus of this Core resource is on how linear and exponential functions can be transformed and how those transformations are represented in graphs, tables, and function rules.

From the Illustrative Mathematics commentary: "This task provides concrete experience with exponential decay. It is intended for students who know what exponential functions are, but may not have much experience with them, perhaps in an Algebra 1 course."

Connect function rules for exponential graphs by connecting to what students know about function transformations and graphs.

This Core resource focuses on students writing function rules for linear and exponential functions based on sequences, graphs, tables, and situations.