Question

Determine whether each function is odd, even or neither.

a) f(x) = -6x^5+2x^3

b) f(x) = x^4-x^2+1

Answer 1

Polynomials with all terms in even degree are even functions, and those with all odd degree terms are odd functions.
For this purpose, a constant k can be considered as k*x^0, so it is even.

A mix of even and odd degree terms is neithter odd nor even.

Example:
f(x)=x^6+x^2+4 is even
f(x)=x^5+x^3+6x is odd
f(x)=x^6+x+1 is neither odd nor even

A test can be applied, which is also the definition of even and odd functions:

if f(-x)=f(x) then f(x)is an even function
if -f(-x)=f(x) then f(x) is an odd function

Answer 2

Even