Let f(x)= 12x^4-x^3

Question

Let f(x)= 12x^4-x^3

Use Algebra to determine if f(x) is even, odd, or neither:

What type of symmetry does the graph f(x) have?:

Answer 1

f(x) = x^4 -x^3

f(-x) = x^4 +x^3 which is not even nor odd

graph it, if symmetric about the y axis, it's even

if symmetric about y=x, it's odd

it's neither

graph it, just no symmetry at all

generally odd degree polynomials are odd functions like cubics or 5d or 7d

and even degree polys are even functions like quadratic parabolas, 4d or 6d

so mixtures of odd and even powers seem to be neither

Answer 2

If f(-x) = f(x), the function is even

If f(-x) = -f(x), the function is odd