Find the domain of the function \( f(x)=\sqrt{2 x+6} \) a) \( [-3, \infty) \) b) \( [3, \infty) \) c) \( (-3, \infty) \) d) \( (-\infty, 3] \) e) \( (-\infty,-3] \)

To find the domain of the function \( f(x)=\sqrt{2x+6} \), we need to ensure that the expression inside the square root is non-negative. So, we set up the inequality: \[ 2x + 6 \geq 0 \] Solving this gives: \[ 2x \geq -6 \] \[ x \geq -3 \] Thus, the domain of the function is \( [-3, \infty) \). So, the correct answer is **a)** \( [-3, \infty) \). Additionally, to make sure you don't accidentally end up with negative values under the square root, always remember to check the critical points derived from your inequality. Using those points can help in visualizing the corresponding intervals where the function behaves as expected! Keep practicing these steps; it makes finding domains a breeze!