Question

How do you determine if `f(x) =root3x` is an even or odd function?

Answer 1

Compare `f(-x)` to `f(x)`.

Explanation:

`f(-x) = root(3)(-x)`

`= - root(3)(x)`

`= -f(x)`

Since `f(-x) = -f(x)`, `f(x)` is an odd function .
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Here is a graph of `y = f(x)`.
graph{root(3)(x) [-10, 10, -5, 5]}
In addition, if `f(x)` is an odd function, if you rotate the graph of `y=f(x)` about the origin by 180 degrees, you will get back the same graph. The graph has rotational symmetry about the origin.