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3.1 Symmetry; Graphing Key Equations
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Symmetry A graph is said to be symmetric with respect to the x-axis if for every point (x,y) on the graph, the point (x,-y) is on the graph.
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A graph is said to be symmetric with respect to the y-axis if for every point (x,y) on the graph, the point (-x,y) is on the graph.
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A graph is said to be symmetric with respect to the origin if for every point (x,y) on the graph, the point (-x,-y) is on the graph.
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Tests for Symmetry x-axisReplace y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the x-axis. y-axisReplace x by -x in the equation. If an equivalent equation results, the graph is symmetric with respect to the y-axis. originReplace x by -x and y by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the origin.
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Not symmetric with respect to the x-axis.
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Symmetric with respect to the y-axis.
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Not symmetric with respect to the origin.
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