As a data analyst reviewing a new predictive model based on the parent radical function $f(x) = \sqrt[3]{x}$, you must document the theoretical limits of the model's inputs and outputs. Based on the fundamental properties of this function, what are its domain and range?

A software developer is documenting the properties of the parent cube root function $f(x) = \sqrt[3]{x}$ for a graphing application. Match each mathematical characteristic of the function to its correct description based on its standard graph and behavior.

A software developer is calibrating a graphing utility to accurately display the parent function $f(x) = \sqrt[3]{x}$. The developer needs to plot five key points derived from perfect cube $x$-values to define the function's S-shaped curve. Arrange these ordered pairs in the correct sequence as they would appear on a graph from left to right (from the smallest $x$-value to the largest $x$-value).

A technical analyst is documenting the properties of the parent cube root function $f(x) = \sqrt[3]{x}$ for a system manual. Because this radical function has a(n) ____ index, the radicand can be any real number, making the domain $(-\infty, \infty)$.

A quality assurance tester reviewing a data algorithm that uses the parent function $f(x) = \sqrt[3]{x}$ should flag negative inputs as errors because the domain of this function is restricted to non-negative numbers.