Find out the symmetry of equations.
y = x^{2} - 6x^{4} + 2
Solution
First we'll check for symmetry around the x-axis. It means that we have to replace all the y's with -y. That's simple enough to do in this case since there is only one y.
- y = x^{2} - 6x^{4} + 2
Now, it is not an equal equation as the terms onto the right are alike to the original equation & the term on the left is the opposite sign. So, this equation doesn't have symmetry around the x-axis.
Next, let's verify symmetry around the y-axis. we'll replace all x's with -x here.
y = ( - x )^{2} - 6 ( - x )^{4} + 2
y = x^{2} - 6x^{4} + 2
Later than simplifying we got precisely the similar equation back out that means that the two are equivalent. Thus, this equation does have symmetry around the y-axis.
At last, we have to check for symmetry around the origin. Here we replace both variables.
- y = ( - x )^{2} - 6 ( - x )^{4 } + 2
- y = x^{2} - 6x^{4} + 2
Thus, as with the first test, the left side is distinct from the original equation & the right side is the same to the original equation. Thus, it isn't equivalent to the original equation & we don't contain symmetry regarding the origin.