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Understanding Symmetry in Graphs: Tests and Equations

Learn about symmetry in graphs with respect to x-axis, y-axis, and origin. Discover how to test for symmetry using equations. Understand the concepts and applications of symmetry in graphing.

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Understanding Symmetry in Graphs: Tests and Equations

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  1. 3.1Symmetry; Graphing Key Equations

  2. 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.

  3. 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.

  4. 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.

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

  6. Not symmetric with respect to the x-axis.

  7. Symmetric with respect to the y-axis.

  8. Not symmetric with respect to the origin.

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