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PP Section 1.7

# PP Section 1.7 - Symmetry and Graphs Circles A graph is...

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Symmetry and Graphs Circles

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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 also on the graph. If a graph is symmetric with respect to the x -axis and the point (3, 5) is on the graph, then (3, -5) is also on the graph.
Example Example 2 y x =

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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 also on the graph. If a graph is symmetric with respect to the y -axis and the point (3, 5) is on the graph then (-3, 5) is also on the graph.
EXAMPLE EXAMPLE 2 x y =

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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 also on the graph. If a graph is symmetric with respect to the origin and the point (3, 5) is on the graph then (-3, -5) is also on the graph.
Example Example 3 x y =

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Test for Symmetry The original equation should NOT change The original equation should NOT change For the x-axis: replace y for –y.
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