Question

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

Answer 1

This function is neither even nor odd.

Explanation:

If a function is odd, `f(-x)=-f(x)`
If a function is even, `f(-x) =f(x)`

For `f(x)=x^3-2`

`f(-x)=(-x)^3-2=-x^3-2`

`f(-x) != -f(x)`, the function is not odd.

`f(-x) !=f(x)`, the function is not even.

The function is neither even nor odd.

You could also examine the graph.

Odd function are symmetric about the origin, i.e. they have the same shape in quadrants 1 and 3, or quadrants 2 and 4.

Even function are symmetric about the y axis, i.e. the graph to the left of the y axis is the mirror image of the graph to the right of the y axis.

If you examine the graph below, it matches neither of these descriptions.graph{x^3-2 [-10, 10, -5, 5]}