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Section 4.7 : Symmetry

Determine the symmetry of each of the following equations.

1. \({x^5} + 5{y^3} = 2y\)
2. \(y + 4{y^2} = 5{x^3} + 1\)
3. \(\displaystyle {y^2} = 8{x^4} + \frac{{{x^2}}}{{{y^2}}} - 1\)
4. \(y = 4{x^2} - 7x + 1\)
5. \(y = 5\left| x \right| + 8\)
6. \(x = 9 - 4{y^2}\)
7. \({y^4} + 8{y^2} = 5x - 1\)
8. \({x^2} - 4xy + {y^2} = 1\)
9. \(\displaystyle y = \frac{{{x^2}}}{{{x^2} + 1}}\)