how to chect weather a given curve is symmetric about any given line

The two sides of a graph of curve, on either side of the axis of symmetry look like mirror images of each other.

Tests for Symmetry :
When you are graphing a relation given by an equation it is helpful to find out first whether its graph has any symmetries. The most common symmetries to look for are symmetry with respect to the x and y axes and the origin:                                                                                                                           
1) A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with -y.

2) A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with -x.

3) A graph will have symmetry about the origin if we get an equivalent equation when all the y’s are replaced with -y and all the x’s are replaced  with  -x

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