There is axis of symmetry in equations that have degree greater than 2 (n > 2)?
How can I find the axis of symmetry in these equation?
There are equations with degree greater than 2 that have not at all axis of symmetry?
Symmetry tests for x-axis, y-axis and about the origin can be found hereHow can I find the axis of symmetry in these equation?
Algebra - Symmetry
Degree is specific to polynomial equations, but the tests above could be for any graph.A graph will have symmetry about the x-axis if we get an equivalent equation when all the y’s are replaced with –y
A graph will have symmetry about the y-axis if we get an equivalent equation when all the x’s are replaced with –x
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.
y = x^4 is an example of a polynomial 'even function' with axis of symmetry about the y-axis. in general, if x^n when n is even, it will be symmetric about the y-axis
y = x^3 is an example of a polynomial 'odd function' that has symmetry about the origin, but doesn't have an "axis of symmetry." In general, if x^n when n is odd, it will be symmetric about the origin.
Do you mean when y = x^6 ?
6 is even, so it will be symmetric about the y-axis. Check using the second test that the graph has symmetry about the y-axis.
y = x^6 + x^3 is one example, an "even" function plus an "odd" polynomial function (x^6, x^3, respectively.)And: Can you an example to equation with non-symmetry axis when n = 6?
https://en.wikipedia.org/wiki/Even_and_odd_functions
The page also includes other ways to determine if functions are "even" or "odd", including basic calculus properties.The sum of an even and odd function is neither even nor odd, unless one of the functions is equal to zero over the given domain.