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# lecture02 - Lecture 2 Graphs in the Plane 2.1 The Cartesian...

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Lecture 2 - Graphs in the Plane 2.1 The Cartesian Plane In this course we will be dealing a lot with the Cartesian plane (also called the xy -plane ), so this section should serve as a review of it and its properties. - 6 ? x -axis y -axis Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 The xy -plane is divided into 4 quadrants by the x -axis and y -axis. Each point in the xy - plane is represented by an ordered pair ( x, y ). If we have two points ( x 1 , y 1 ), ( x 2 , y 2 ) in the xy -plane, then: the distance d between them is found using the Pythagorean theorem. The formula is: d = p ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 the midpoint between them is found by averaging the x -coordinates and then averaging the y -coordinates. The formula is: P = x 1 + x 2 2 , y 1 + y 2 2

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s s s d ( x 1 , y 1 ) ( x 2 , y 2 ) P | y 1 - y 2 | | x 1 - x 2 | A A A U 2.2 Graphs of Functions and Equations In this section we review the graphing of functions. Example: Graph the function y = | x | = ( x if x 0 - x if x 0 solution: - 6 ? @ @ @ @ @ @ @ @ y = x y = - x
Example: Graph the function y = | x | - 2. solution: The effect of the - 2 is to shift the graph down 2 units: Terminology: x -intercepts - place or places where the graph crosses the x -axis. There could be several

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lecture02 - Lecture 2 Graphs in the Plane 2.1 The Cartesian...

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