Problem 10 - Algebra 1: Concepts and Skills

Question

Find the domain and the range of the function. $$y=\sqrt{x}$$

Step-by-Step Solution

Answer

The domain of the function \(y = \sqrt{x}\) is [0, ∞), and the range of the function is [0, ∞).

Step 1: Find the domain

Start by finding the domain of the function. Because the square root of a real number is only defined for non-negative values, the domain of the function \(y = \sqrt{x}\) is x >= 0. In interval notation, this would be written as [0, ∞).

Step 2: Find the range

Next, determine the range of the function. The square root function always returns a non-negative value. Therefore, the range of the function \(y = \sqrt{x}\) is y >= 0. In interval notation, this would be [0, ∞).