Write the domain and range for the square root function \( y=\sqrt{3 x-2}+4 \) in interval notation. (1 point) domain: \( \left[\frac{2}{3}, \infty\right) \), range: \( [4, \infty) \) domain: \( [4, \infty) \), range: \( \left[\frac{2}{3}, \infty\right) \) domain: \( (4, \infty) \), range: \( \left(\frac{2}{3}, \infty\right) \) domain: \( \left(\frac{2}{3}, \infty\right) \), range: \( (4, \infty) \)

To find the domain of \( y = \sqrt{3x - 2} + 4 \), we need to ensure that the expression inside the square root is non-negative. This leads to the inequality \( 3x - 2 \geq 0 \), which solves to \( x \geq \frac{2}{3} \). Therefore, the domain is \( \left[\frac{2}{3}, \infty\right) \). The range can be determined by considering the behavior of the square root function. The minimum value occurs when \( x = \frac{2}{3} \), giving \( y = \sqrt{0} + 4 = 4 \). As \( x \) increases, \( y \) will also increase without bound. Thus, the range is \( [4, \infty) \).