## Algebra and Trigonometry 10th Edition

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.