Not sure how to do this:

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = -9 x^3 + 8x

Would it be odd because the answer will always come out odd whether there is a -x or x?

Question

Not sure how to do this: 

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = -9 x^3 + 8x

Would it be odd because the answer will always come out odd whether there is a -x or x?

anonymous · Answer

first off it is clearly "odd" because it is a polynomial with only odd exponents

anonymous · Answer

but your teacher wants you to do this:
$$f(-x)=9(-x)^3+8(-x)=-9x^3-x=-(9x^3+x)=-f(x)$$ and so since 
$$f(-x)=-f(x)$$ it is odd

anonymous · Answer

Ok, got it thank you very much.

anonymous · Answer

typo there
i meant $$f(-x)=9(-x)^3+8(-x)=-9x^3-8x=-(9x^3+8x)=-f(x)$$

anonymous · Answer

yw