Definition: A radical function is a function in which the independent variable is in the radicand (under the radical (√) symbol):

$\dpi{150} \bg_white \\y = \sqrt x\\ y = \sqrt[3]{x}$

Many people mistakenly call this a ‘square root’ symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root or higher.

Parent graph of a square-root function:

Parent graph of a cube-root function:

Example: Find the domain: f(x) = √(x – 4)

Solution:

Because we can only take the square root of values greater than or equal to 0, x – 4 must be greater than or equal to 0.

x – 4 ≥ 0

x ≥ 4

The domain must be all values of x greater than or equal to 4 in order for us to be able to take the square root.