Question

Algebraically determine if the relation x = – y2 – 0.1 is symmetrical with respect to the x-axis, y-axis, or the origin.

Answer 1

1. Replace x by -x in the relation x = –y^2 – 0.1. If you get the SAME relation, then it is symmetric about the y-axis.

2. Replace y by -y in the relation x = –y^2 – 0.1. If you get the SAME relation, then it is symmetric about the x-axis.

3. IF it is symmetric about the x-axis AND the y-axis, then it is symmetric about the origin.