Unformatted text preview: ry 25, 2010 xii Preface Chapter 1 Relations and Functions
1.1 The Cartesian Coordinate Plane In order to visualize the pure excitement that is Algebra, we need to unite Algebra and Geometry.
Simply put, we must ﬁnd a way to draw algebraic things. Let’s start with possibly the greatest
mathematical achievement of all time: the Cartesian Coordinate Plane.1 Imagine two real
number lines crossing at a right angle at 0 as below.
1 −4 −3 −2 −1 1 2 3 4 x −1
−4 The horizontal number line is usually called the x-axis while the vertical number line is usually
called the y -axis.2 As with the usual number line, we imagine these axes extending oﬀ indeﬁnitely
in both directions. Having two number lines allows us to locate the position of points oﬀ of the
number lines as well as points on the lines themselves.
2 So named in honor of Ren´ Descartes.
The labels can vary depending on the context of application. 2 Relations and Functions For example, consider the point...
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