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A Geometric Approach to Linear Functions

by Jack E. Graver (Syracuse University)

This article originally appeared in:
College Mathematics Journal
November, 1995

Subject classification(s): Algebra and Number Theory | Linear Algebra | Linear Transformations | Geometry and Topology | Analytic Geometry | Lines
Applicable Course(s): 2.1 College Algebra | 3.1 Mainstream Calculus I

There are three somewhat distinct topics in this article: the condition for linear functions to commute, a linear function as a transformation of the number line, and linear difference equations. A linear function \(y=f(x)=ax+b\) can be characterized in terms of slope and the “center of reflection,” both of which reflect the geometric property of the function.


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Capsule Course Topic(s):
Linear Algebra | Geometry
Linear Algebra | Linear Transformation
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