Question

How do you know if `f(x) = 5x^6 + 8x^2 – 16` is an even or odd function?

Answer 1

`f(x)` is even.

Explanation:

A function `f(x)` is even if and only if `f(-x) = f(x)`.
A function `f(x)` is odd if and only if `f(-x) = -f(x)`

In this case
`f(-x) = 5(-x)^6 + 8(-x)^2 - 16 = 5x^6 + 8x^2 - 16 = f(x)`

So `f(x)` is even.

(In general, this kind of function can be easily identified as even or odd, as if every term in a sum is even, then so is the sum, and if every term in a sum is odd, then so is the sum).