which of the following is the graph of this square root function? f(x) = √(x - 4)+3

Answer:

The domain of (y = \sqrt{x - 4}+3) is (x\geq4) since the expression under the square - root must be non - negative ((x - 4\geq0)). When (x = 4), (y=\sqrt{4 - 4}+3=3). The graph is a square - root function that is shifted 4 units to the right and 3 units up from the parent function (y = \sqrt{x}). Without seeing the full options, the correct graph should start at the point ((4,3)) and increase as (x) increases. If we assume the third graph (from left to right) has its starting point at ((4,3)) and is an increasing curve for (x\geq4), then that is the correct graph. But since no labels are given for the options, a more general description is: The graph has a starting point at the point ((4,3)) (the x - intercept of the expression inside the square root is (x = 4) and when (x = 4), (y = 3)), and is an increasing curve for (x\geq4) with a domain of (x\in[4,\infty)) and a range of (y\in[3,\infty)).