This problem concerns even and odd functions. Recall that a function $f$ is even if $$f(x) = f(-x)$$ for all $x$ in its domain, and it is odd if $$f(x) = -f(-x)$$ for all $x$ in its domain. The graph of an even functions is symmetric with respect to the $y$-axis, and an odd function is symmetric with respect to the origin. This is an example of one of our major themes: the interplay between algebra and geometry.
For each of the following functions enter "E" to indicate that the function is even, "O" to indicate it is odd, and "N" to indicate that is neither even nor odd.

1. $f(x) = x^ {8 } - 6x^ {6 } +3x^ {2 }$
2. $f(x) = -5x^ {8 }- 3x^ {6 } -2$
3. $f(x) = x^ {3 } + x^ {3 } +x^ {7 }$
4. $f(x) = x^ {8 } +3 x^ {6 } +2x^ {7 }$