Symmetry

The graph of an equation may be symmetrical over the x-axis, the y-axis and/or the origin.  Knowing if a graph is symmetrical helps make it easier to sketch the graph of an equation. 

To test for x-axis symmetry, you need to replace y with –y.  If the new equation is identical to the original equation, then the graph is symmetrical over the x-axis.

To test for y-axis symmetry, you replace x with –x.  If the new equation is identical to the original equation, then the graph is symmetric over the y-axis.

To test for symmetry over the origin, you replace x with –x, and y with –y.  Again if the equation is identical to the original equation, then the graph is symmetric over the origin.

The linear equations y = x  or  y = -x  are the only two equations which are symmetric over the origin.

The equation for a circle with centre (0.0) is symmetric over the x-axis, the y-axis and the origin.

Filed under: Functions and Their Graphs

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