Find the domain of the following function.
$y=\sqrt{x-3}$

• A. $(-\infty ,3]$
• B. $(-\infty ,-3)\cup (-3,\infty )$
• C. $[3,\infty )$
• D. $(-\infty ,\infty )$

Answer: (C)

Verified step by step guidance

1. Identify the function given: \(y = \sqrt{x - 3}\). Since this is a square root function, the expression inside the square root (called the radicand) must be greater than or equal to zero for the function to be defined.
2. Set up the inequality for the radicand: \(x - 3 \geq 0\). This ensures the value inside the square root is not negative.
3. Solve the inequality: Add 3 to both sides to isolate \(x\), giving \(x \geq 3\).
4. Interpret the solution: The domain includes all real numbers \(x\) such that \(x\) is greater than or equal to 3. This means the function is defined starting at 3 and continues to infinity.
5. Express the domain in interval notation: The domain is \([3, \infty)\), where the square bracket indicates that 3 is included in the domain and the parenthesis indicates that infinity is not a number but a direction.