Question

Why does a radical function with an even index only appear on one sode of the x-axis while a radical woth an odd index appears on both sides?

Answer 1

The right side of the x-axis represents positive domain and the left side of the x-axis represents a negative domain.

So a radical function with an even index could have a domain of x≥0, so that's why they only appear on the right side.

Whereas a radical function with an odd index has a domain of all real numbers, so they appear on both sides.

The easiest scenario to see why this is true is to test square root and cube root.

You can't have a square root (even index) of a negative number, but you can have a cube root (odd index) of a negative number.

Example: $\sqrt{-9}$ = UNDEFINED,     ರ_ರ

$\sqrt[3]{-27} = -3$,     ♥‿♥