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# 1.3 SYMMETRY

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### 1.3 SYMMETRY

1. 1. 1.3Symmetry<br />
2. 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. <br />x-Axis Symmetry<br />
3. 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.<br />y-Axis Symmetry<br />
4. 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.<br />origin Symmetry<br />
5. 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. <br />Tests for Symmetry<br />y-axis Replace x by -x in the equation. If an equivalent equation results, the graph is symmetric with respect to the y-axis.<br />origin Replace x by -xandy by -y in the equation. If an equivalent equation results, the graph is symmetric with respect to the origin.<br />
6. 6. Not symmetric with respect to the x-axis.<br />
7. 7. Symmetric with respect to the y-axis. <br />
8. 8. Not symmetric with respect to the origin.<br />