A1.F.2.1  Distinguish between linear and nonlinear (including exponential) functions arising from realworld and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals.
In a Nutshell
Students will distinguish and describe functions as linear or nonlinear functions. Using their knowledge acquired during this unit the students will determine whether linear equations are functions. Students will use tables, graphs, and equations to identify characteristics of nonlinear functions. Realworld situations are useful for students to understand the equal intervals that functions tend to grow. Graphing and creating tables for various equations can show how exponential functions grow as equal factors over equal intervals. Parent functions of other graphs will be introduced in order to determine the differences of linear and nonlinear.
Student Actions

Teacher Actions

 Develop accurate and appropriate procedural fluency by creating tables, writing equations, and graphing functions to determine linear and nonlinear relationships.
 Develop a Deep and Flexible Conceptual Understanding by exploring linear and nonlinear functions to understand the relationship between the independent and dependent variables.
 Students will Develop Mathematical Reasoning by recognizing every input having exactly one output is essential in a function. Students must understand that changing the input leads to a change in the output.


Use and connect mathematical representations by engaging students to connect the concepts of linear and nonlinear functions to their equations, graphs, tables, and charts.

Pose purposeful questions and examples to connect students to realworld situations by using examples of several different functions as they explore the similarities and differences of those functions.
 Implement tasks that promote reasoning and problem solving byhaving students interpret the mathematical relationship of tables, graphs, and equations of linear or nonlinear functions.

Key Understandings

Misconceptions

 Piecewise linear function is a realvalued function defined on the real numbers or a segment thereof, whose graph is composed of straightline sections.

 Students confuse or can not identify the part of the domain which corresponds to each piece of the function.

Students interchange the domain and range of each piece(s).

Students tend to think that a piecewise linear function has only one linear function because of its name. They fail to realize that two or more distinct lines are needed to represent a realworld situation.

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