Understanding the Connections between Equations and Graphs (CoRD)
Monty Harper, Oklahoma State University
Deborah Moore-Russo, University of Oklahoma
In order to develop a robust understanding of functions, students must be able to navigate between the different representations of functions. This CoRD is targeted to help students develop a deeper understanding of how algebraic equations and graphs are related. This is done through a series of activities that use active exploration in digital environments that consider symmetry in even and odd functions as well as the role that linear factors play in polynomials and rational functions.
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Categorizing Shapes and Functions by Symmetry
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Students explore different types of symmetry using letter tiles then apply what they have learned to categorize graphs of functions by symmetry.
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Developing Algebraic Tests for Even and Odd Functions Developing an Algebraic Test Lesson Plan Even and Odd Functions Worksheet Graphing Bingo Activity Lesson Plan
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Students develop an algebraic test to determine whether a given function is even, odd, or neither. Students to use their knowledge of even and odd for fun in a function graphing competition.
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Combining Linear Factors – Polynomials from Sums and Products Zeros of Polynomials Worksheet Zeros of Polynomials Answer Key
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Students explore the relationships between linear factors of a polynomial function and the x-intercepts of its graph.
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Rational Functions and Asymptotes
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This lesson focuses on rational functions formed by dividing a constant or a linear function by a product of linear factors (each of which differs from the numerator). Students will explore the relationships between factors of the numerator and denominator of a rational function and the function’s zeros and its domain (including vertical asymptotes) both algebraically and graphically.
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More on Domains of Rational Functions (Introducing Holes) Rational Functions’ Domains Worksheet Rational Functions’ Domains Answer Key
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This lesson focuses on rational functions with at least one common linear factor in the numerator and denominator. Students explore the relationships between factors of the numerator and denominator of a rational function and the function’s zeros and its domain (including its “holes”) both algebraically and graphically.
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This work is licensed under CC BY-NC-SA 4.0
