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| Functions |
 Cartesian Coordinate System Domain and Range Inverse Functions Even-Odd Symmetry of Functions Periodicity of Functions
Exponential Functions Logarithmic Functions Natural Logarithms
Hyperbolic Functions |
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Coordinate systems are used to define the position of a point in space. One-dimensional space: a straight line. In order to describe the position of a point on a line, one can use a number line, that is, a straight line, on which the origin and a scale are established. Every point on the number line corresponds to a unique real number, which is called the coordinate (or x-coordinate) of the point.
Two-dimensional space: a plane. Each point in a plane is determined by an ordered pair of numbers. To describe the position of that point, one has to use two number lines in the plane, one horizontal and one vertical. These two perpendicular lines make up the axes of the Cartesian coordinate system, the origin of which is the intersection point of the lines. The horizontal line is called the x-axis. The vertical line is called the y-axis. Both lines, horizontal and vertical, are said to be the coordinate axes. The projections of a point onto the coordinate axes are called the coordinates of the point. The set of coordinates is denoted as the ordered pair ( x, y ). The origin is assigned the number pair (0,0), which is symbolized for short as 0.
The x-coordinate (or abscissa)
describes the position of the point from the origin along the x-axis. The x-coordinates of points are positive to the right and negative to the left from the origin. The y-coordinates of points are positive going up and negative going down from the origin. The coordinate axes divide the x,y-plane into four quadrants, which are numbered by Roman figures, one to four, moving counter-clockwise.
Three-dimensional space.
Each space point is determined by an ordered number triple, and correspondingly, the Cartesian coordinate system involves three coordinate axes. To form a three-dimensional Cartesian system of coordinates, we need only to enlarge the two-dimensional coordinate system, adding the z-axis, which passes through the origin perpendicularly to the x,y-plane.
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