reflections

reflections - Reflections of graphs in the x and y axes...

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Reflections of graphs in the x and y axes Introductory example . Suppose that we have already constructed a table of values for the graph of the equation = y + x 4 and that we wish to draw the graph of = y - + x 4. For each point ( ) , x 1 y 1 on the graph of = y + x 4 we can obtain a corresponding point ( ) , x 1 - y 1 on the graph of = y - + x 4 by just changing the sign of the y coordinate of the first point. x | - 4 - 15 4 - 3 - 7 4 0 9 4 5 33 4 12 = y + x 4 | 0 1 2 1 3 2 2 5 2 3 7 2 4 = y - + x 4 | 0 - 1 2 - 1 - 3 2 2 - 5 2 - 3 - 7 2 - 4 The vertical line joining two points ( ) , x 1 y 1 and ( ) , x 1 - y 1 is bisected by the x axis. We may say that the second point ( ) , x 1 - y 1 is the reflection of the first point ( ) , x 1 y 1 in the x axis as a " mirror line ". It should be thought of as a two sided mirror so that also the first point ( ) , x 1 y 1 is the reflection of the second point ( ) , x 1 - y 1 . In the following picture the graph of = y - + x 4 ( blue graph) is the reflection in the x axis of the graph of = y + x 4 ( red graph). Suppose that we have already constructed a table of values for the graph of the equation = y + x 4 and that we wish to draw the graph of = y - + x 4. The second equation is obtained from the first by replacing x by its additive inverse - x . For each point ( ) , x 1 y 1 on the graph of = y + x 4 we can obtain a corresponding point ( ) , - x 1 y 1 on the graph of = y - + x 4 by just changing the sign of the x coordinate of the first point. Thus we can obtain a table of values for plotting = y - + x 4 by changing the sign of the x coordinates in the table used for the first graph. The horizontal line joining two points ( ) , x 1 y 1 and ( ) , x 1 - y 1 is bisected by the y axis. The second point ( ) , - x 1 y 1 is the reflection of the first point ( ) , x 1 y 1 in the y axis as a " mirror line ". Thus the table . . . x | - 4 - 15 4 - 3 - 7 4 0 9 4 5 33 4 12 = y + x 4 | 0 1 2 1 3 2 2 5 2 3 7 2 4
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gives rise to the table . . . x | 4 15 4 3 7 4 0 - 9 4 - 5 - 33 4 - 12 = y - + x 4 | 0 1 2 1 3 2 2 5 2 3 7 2 4 Rearranging the values in the new table in reverse order so that the x coordinates are increasing from left to right gives the following table. x
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This note was uploaded on 11/12/2011 for the course MATH 111 taught by Professor Uri during the Spring '08 term at Rutgers.

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reflections - Reflections of graphs in the x and y axes...

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