# 6: Functional Analysis

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• 6.1: Rectangular Coordinate System
The rectangular coordinate system consists of two real number lines that intersect at a right angle. The horizontal number line is called the x -axis, and the vertical number line is called the y-axis. These two number lines define a flat surface called a plane, and each point on this plane is associated with an ordered pair of real numbers (x,y). The first number is called the x-coordinate, and the second number is called the y-coordinate. The intersection is the origin: (0,0).
• 6.2: Relations and Functions
• 6.3: The Graph of a Function
Descartes introduces his coordinate system, a method for representing points in the plane via pairs of real numbers. Indeed, the Cartesian plane of modern day is so named in honor of Rene Descartes, who some call the “Father of Modern Mathematics.” A Cartesian Coordinate System consists of a pair of axes, usually drawn at right angles to one another in the plane, one horizontal (labeled x) and one vertical (labeled y).

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