Here are the essential concepts you must grasp in order to answer the question correctly.
Symmetry in Graphs
Symmetry in graphs refers to the property where a graph remains unchanged under certain transformations. For example, a graph is symmetric with respect to the x-axis if replacing y with -y yields the same equation. Similarly, it is symmetric with respect to the y-axis if replacing x with -x gives the same equation, and it is symmetric with respect to the origin if replacing both x and y with their negatives results in the same equation.
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Graphs and Coordinates - Example
Absolute Value Functions
Absolute value functions, denoted as |x|, represent the distance of a number from zero on the number line, always yielding non-negative outputs. In the context of the equation |x| = |y|, this means that both x and y can take on positive or negative values, leading to a relationship that can be visualized in the coordinate plane, often resulting in a 'V' shape or lines that reflect symmetry.
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Testing for Symmetry
To determine the symmetry of a graph, specific tests can be applied. For x-axis symmetry, substitute y with -y; for y-axis symmetry, substitute x with -x; and for origin symmetry, substitute both x and y with their negatives. If the original equation holds true after these substitutions, the graph exhibits the corresponding symmetry. This method is essential for analyzing the given equation |x| = |y|.
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