Question

How do you determine if `-2x^4-4x+6` is an even or odd function?

Answer 1

neither even nor odd.

Explanation:

To determine if a function is even/odd consider the following.

• If f(x)=f( -x) , then f(x) is even

Even functions are symmetrical about the y-axis.

• If f( -x) = - f(x) , then f(x) is odd

Odd functions have half-turn symmetry about the origin.

Test for even

`f(-x)=-2(-x)^4-4(-x)+6=-2x^4+4x+6`

Since f(x) ≠ f( -x) , then f(x) is not even

Test for odd

`-f)x)=-(-2x^4-4x+6)=2x^4+4x-6`

Since - f(x) ≠ f( -x) , then f(x) is not odd

Thus function is neither odd nor even.
graph{-2x^4-4x+6 [-20, 20, -10, 10]}