The document discusses three types of symmetry for graphs: x-axis symmetry, where (x,y) corresponds to (x,-y); y-axis symmetry, where (x,y) corresponds to (-x,y); and origin symmetry, where (x,y) corresponds to (-x,-y). It provides tests for each type of symmetry by replacing variables in the graphing equation. An example at the end finds no x-axis or origin symmetry but y-axis symmetry.

1. 1.3Symmetry

2. 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. x-Axis Symmetry

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.y-Axis Symmetry

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.origin Symmetry

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