Question

Find the domain and range of radical function

Answer 1

The domain of a radical function depends on the type of root and the expression under the root. The range of a radical function depends on the shape of the graph. Generally, the domain is the set of all possible output values, while the range is the set of all possible input values.

Step-by-step explanation:

A radical function is a function that contains a square root or other root. The domain of a radical function depends on the type of root and the expression under the root. For example, the domain of the function √x is all real numbers because the square root of any non-negative number is defined. However, the domain of the function √(x-2) is x ≥ 2 because the expression under the square root must be non-negative.

The range of a radical function depends on the shape of the graph. If the function has a vertical stretch or compression, the range will be affected accordingly. Generally, the domain of a radical function is the set of all possible output values, or y-values, while the range is the set of all possible input values, or x-values. The range can be determined by analyzing the graph or algebraically solving for y.

Answer 2

The radical function is 3√x + 1.

Since the cubic root of zero is zero, 0 would be x.

Add zero and one, which gives you 1. 1 is y.

You get (0,1)

Since this is a positive radical, it would be going to the top right.

So, the domain is x ≥ 0

the range is y ≥ 1