Understanding Radical Functions

The video tutorial explains how to find the domain and range of radical functions. It covers the importance of the index being even or odd, affecting the domain and range. Examples include square root, cube root, and fourth root functions, demonstrating how to solve inequalities and use interval notation. Graphs are used to verify the domain and range for each function.

What is the domain of a radical function?

• The set of all negative numbers

• The set of all positive numbers

• The set of all possible inputs

• The set of all possible outputs

How does the index of a radical function affect its domain?

• It has no effect on the domain

• It changes the shape of the graph

• It affects whether the radicand can be negative

• It determines the color of the graph

For a square root function, what must be true about the radicand?

• It must be greater than zero

• It must be less than zero

• It can be any real number

• It must be greater than or equal to zero

What is the range of a square root function?

• Only positive numbers

• Only negative numbers

• All real numbers

• Non-negative numbers

What is the domain of a cube root function?

• Only positive numbers

• Non-negative numbers

• Only negative numbers

• All real numbers

What is the range of a cube root function?

• Only positive numbers

• Only negative numbers

• Non-negative numbers

• All real numbers

For a fourth root function, what must be true about the radicand?

• It must be less than zero

• It must be greater than zero

• It must be greater than or equal to zero

• It can be any real number

What is the domain of the fourth root function discussed?

• X is less than or equal to 3

• X is greater than or equal to -3

• X is less than or equal to -3

• X is greater than or equal to 3

What is the range of the fourth root function discussed?

• Only negative numbers

• All real numbers

• Only positive numbers

• Non-negative numbers

How can you verify the domain and range of a function?

• By checking the color of the graph

• By counting the number of roots

• By projecting the graph onto the axes

• By measuring the length of the graph