On what interval is the square root function \( y=\sqrt{2 x+6}+4 \) increasing? (1 point) The function is increasing over the interval \( [\square, \infty) \). Check answer Remaining Attempts : 3

To find where the function \( y = \sqrt{2x + 6} + 4 \) is increasing, we can analyze the expression inside the square root. The function is defined for \( 2x + 6 \geq 0 \), which simplifies to \( x \geq -3 \). Since the square root function always has a positive derivative when we are in its domain, and since adding 4 is a constant shift upwards, we know that the function is indeed increasing for all \( x \) in the interval \( [-3, \infty) \). So, the function is increasing over the interval \( [-3, \infty) \). To check common mistakes, many students might overlook the domain of the square root function. Always ensure you define the domain before analyzing the intervals of increase or decrease. If you forget to check for where the function is defined, you could misidentify the intervals!