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.
