What is the domain of the following function? \( y=\sqrt{x+3} \) Answer Attempt 1 out of 2 \( \begin{array}{ll}{[3, \infty)} & {[-3, \infty)} \\ (\infty, 3] & (\infty,-3]\end{array} \)

To determine the **domain** of the function \( y = \sqrt{x + 3} \), we need to identify all real numbers \( x \) for which the expression inside the square root is **non-negative** (since the square root of a negative number is not a real number). ### Step-by-Step Reasoning: 1. **Identify the Expression Inside the Square Root:** \[ x + 3 \] 2. **Set the Expression Inside the Square Root to Be Greater Than or Equal to Zero:** \[ x + 3 \geq 0 \] 3. **Solve for \( x \):** \[ x \geq -3 \] ### Conclusion: - The function \( y = \sqrt{x + 3} \) is defined for all real numbers **greater than or equal to** \(-3\). - Therefore, the **domain** of the function is: \[ [-3, \infty) \] ### Matching with the Provided Options: From your provided answer attempts: \[ \begin{array}{ll} {[3, \infty)} & {[-3, \infty)} \\ {(\infty, 3]} & {(\infty,-3]} \end{array} \] The correct domain corresponds to: \[ [-3, \infty) \] **Therefore, the domain of the function \( y = \sqrt{x + 3} \) is \([-3, \infty)\).**