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
Determine whether each function is odd, even or neither.
a) f(x) = -6x^5+2x^3
b) f(x) = x^4-x^2+1
2 answers
Even