Question

How do you know if `f(x) = 13x^4 – 2x^3 + 7x` is an even or odd function?

Answer 1

`f(x)` is neither even nor odd.

Explanation:

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

To see which (if any) is the case here, we simply look at `f(-x)`.

`f(-x) = 13(-x)^4 - 2(-x)^3 + 7(-x) = 13x^4 + 2x^3 - 7x`

As `f(x) = 13x^4 - 2x^3 +7x`
and `-f(x) = -13x^4 + 2x^3 -7x`

we have that
`f(-x) != f(x)` and `f(-x) != -f(x)`

So `f(x)` is neither even nor odd.