Question

Determine whether the following function is even, odd, or neither f(x)=x^5-x^3-1

Answer 1

For a function to be classified as even, the number with the largest exponent must have an even exponent and be symmetrical along the y-axis. This equation's largest exponent is an odd number, so this function is not even.
For a function to be classified as odd, the number with the largest exponent must have and odd exponent. This equation's largest exponent is odd. However, for a function to be odd, it needs to have its center at the origin. As you can see in the equation, the final value shifts the equation vertically, making it asymmetrical about the origin. That makes this function not odd.
Since this function isn't even nor odd, it is neither.

Answer 2

easy way to check:

even --> f(-x) = f(x)

odd ---> -f(-x) = f(x)