Find the domain of the function. \[ v(x)=\sqrt{21+3 x} \] Write your answer using interval notation.

To find the domain of the function \( v(x) = \sqrt{21 + 3x} \), we need to ensure that the expression inside the square root is non-negative, since the square root function is only defined for non-negative values. We set up the inequality: \[ 21 + 3x \geq 0 \] Now, we solve for \( x \): 1. Subtract 21 from both sides: \[ 3x \geq -21 \] 2. Divide both sides by 3: \[ x \geq -7 \] This means that \( x \) must be greater than or equal to \(-7\). In interval notation, the domain of the function is: \[ [-7, \infty) \] Thus, the domain of \( v(x) \) is \(\boxed{[-7, \infty)}\).