#### Answer

Odd functions have only variables raised to odd powers.
Even functions have only variables raised to even powers.

#### Work Step by Step

Determine which functions are odd and which are even:
$f(x)=x^2-x^4$
$g(x)=2x^3+1$
$h(x)=x^5-2x^3+x$
$j(x)=2-x^6-x^8$
$k(x)=x^5-2x^4+x-2$
$p(x)=x^9+3x^5-x^3+x$
Graph the 6 functions.
The functions whose graphs are symmetric with respect to the origin are odd: $h(x),p(x)$.
The functions whose graphs are symmetric with respect to the $y$-axis are even: $f(x),j(x)$.
The functions which are neither odd, nor even are: $g(x),k(x)$.
We notice that we have:
- the equations of even functions contain only even powers of $x$
- the equations of odd functions contain only odd powers of $x$
- the equations which have variables raised to even and odd powers are neither odd, nor even.