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Use the structure of a visual pattern to find the value of the 6th term of a linear sequence.

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 start by creating definitions of linear and exponential functions by analyzing examples and non-examples of these types of functions. Students then use what they have learned about linear and exponential functions to solve word problems related to these function types. What is not 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.

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.

Students will make connections between examples of verbal descriptions of the relationship between x and y and their corresponding graphs, using structural elements of linear relationships.

Use what students know about tables and finding rate of change to connect exponential functions to their function rules.

Compare tables for linear and exponential functions to distinguish their tables and function rules.

Use what students know about tables and rate of change to connect these tables to linear function rules.

Students will look for connections between linear equations and visual sequences in order to learn how to chunk visual sequences and linear equations into parts that grow and parts that do not change. This involves one pair of students manipulating an interactive applet while other students watch and make their own connections with a partner.

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

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.