Question

I give medals and fans!

Determine whether the function ƒ(x) = x^4 − 4x^2 − 1 is even, odd or neither.

odd
even
neither

I think I know the answer, I just need to clarify.

Answer 1

I never got a medal or fan... quit lying to people . >:/

Answer 2

Ya happy now? @DanielTosh

Answer 3

Yes. Yes I am. :)

Answer 4

Good !

Answer 5

\[\large f(x) = x^4 − 4x^2 − 1\]Here is another way we can interpret that last term.\[\large f(x) = x^4 − 4x^2 − 1x^0\]

Hmm they appear to be all even powers on x, don't they? :)

Answer 6

whether a polynomial function is odd or even depends on it's order. The order is the highest exponent in the polynomial. In this case it is 4.

If the order is an odd number, the function is odd.
If the order is even, the function is even.

This case, it is even since it's fourth order.

Answer 7

If the function is odd \[f(-x)=-f(x)\]
If the function is even \[f(-x)=f(x)\]
So find f(-x)\[f(-x)=(-x)^4-4(-x)^2-1=x^4-4x^2-1=f(x)\]
Therefore it is an even function.

Answer 8

Thank you all so much!(: