3.1 Symmetry Graphing Key Equations

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3.1Symmetry 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-axis Replace y buy -y in the equation. If an
  equivalent equation results, the graph is
  symmetric with respect to the x-axis.
• y-axis Replace x buy -x in the equation. If an
  equivalent equation results, the graph is
  symmetric with respect to the y-axis.
• origin Replace x buy -x and y buy -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.