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Graphing an equation involving absolute value in the plane

# Graphing an equation involving absolute value in the plane...

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Graphing an equation involving absolute value in the plane Graph the equation: . Background: Consider the graph of , where denotes the absolute value of . Note that can never be negative and that the smallest value of occurs at . Plotting points on the graph near , and drawing two rays from that contain all these points, we obtain the graph of : Note that the graph of has a "V shape." It turns out that the graph of any equation of the form , with , will also have such a shape-- either or . Moreover, the vertex of the "V shape" occurs at the -value that makes the expression within the absolute value, , equal to . Therefore, to graph functions of the form , we first plot the vertex and at least one point on each side of the vertex. We then draw rays originating from the vertex that contain these

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Unformatted text preview: points. The current problem: To graph , we first find the vertex. As explained above, the -value of the vertex is such that , and so . To obtain the -value of the vertex, we evaluate at : Figure 1 . So the vertex of the graph occurs at . Next we find a point on the graph on each side of the vertex. For , we have . So the point is on the graph. For , we have . So the point is also on the graph. Drawing rays from the vertex through the points and , we obtain the graph of . Note that when drawing these graphs, it is very important that we do not extend the rays below the vertex . For additional explanation, see your textbook: • Section 2.2: Graphs of Functions...
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Graphing an equation involving absolute value in the plane...

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