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# A1-F-2-1

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on November 21, 2016 at 12:36:45 pm

A1.F.2.1 - Distinguish between linear and nonlinear (including exponential) functions arising from real-world 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. Real-world 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.

## 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.
• Give students the opportunity to use and connect mathematical representations from a real-world graph  to a data sets, a verbal interpretation or a piecewise function.

• Build procedural fluency from conceptual understanding as students read only a segment of a linear graph to interpret and express the boundaries of each piece of the function.
• Pose purposeful questions to students about what they notice on the graph about the domain, range and the pieces how they relate to a real-world situation.

## Misconceptions

• Piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line 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 real-world situation.

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