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

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

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 \(x - 3 \geq 0\) by adding 3 to both sides, resulting in \(x \geq 3\).
4. Interpret the solution: the domain of the function includes all real numbers \(x\) such that \(x\) is greater than or equal to 3.
5. Express the domain in interval notation as \(\left[3, \infty\right)\), which means the function is defined for all \(x\) starting at 3 and extending to positive infinity.