# Why does a radical function with an even index only appear on one side of the x-axis while a radical function with an odd index appears on ?

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

### 2 Answers

- mizooLv 74 weeks ago
The radical with the even index has a restriction in the domain : The expression inside the radical must be greater than or equal to zero.

The radical with odd index doesn't have this restriction => the graph appears on both sides.

- llafferLv 74 weeks ago
f(x) = √x

Using that as an example, if x is negative we don't get a real value for f(x) since we can't get the square root of a negative number.

So f(x) has no real values when x < 0, so that's why the graph only exists when x >= 0.

When you have cube root,

f(x) = ³√x

the cube root of a negative number results in a negative real value, so this can be graphed for all values of x.