Question

How do you determine if `g(x)=3x^5+2x` is an even or odd function?

Answer 1

`g(x)` is an odd function.

Explanation:

The quick way to determine whether a polynomial function is odd or even is to check whether all of its terms are of odd or even degree.

In our example, both `3x^5` and `2x` are of odd degree, so the function is odd.

In general:

• An even function is a function satisfying `f(-x) = f(x)` for all `x` in its domain.
• An odd function is a function satisfying `f(-x) = -f(x)` for all `x` in its domain.

In our example:

`g(-x) = 3(-x)^5+2(-x) = -3x^5-2x = -(3x^5+2x) = -g(x)`

So `g(x)` is an odd function.