Find the domain of the function. \( f(x)=\sqrt{3 x-12} \) The domain is \( \square \). (Type your answer in interval notation.)

To determine the domain of the function \( f(x) = \sqrt{3x - 12} \), we need to ensure that the expression inside the square root is non-negative. This means solving the inequality: \[ 3x - 12 \geq 0 \] Solving for \( x \), we get: \[ 3x \geq 12 \] \[ x \geq 4 \] Thus, the domain of the function in interval notation is \( [4, \infty) \). To help remember this kind of problem, always look for what values you can input into the function. For square roots, you want the radicand (the expression inside the square root) to be greater than or equal to zero. It's like ensuring your adventure starts with a solid ground—no one wants to trip over an imaginary number! Additionally, when you encounter expressions like this, it can be helpful to sketch the function or at least analyze its behavior near the edges of the domain. You'll notice how the graph looks only starting from that point (here, x = 4) and heads toward positive infinity! This visual can really cement your understanding of where your function "comes alive."