Final answer:
The correct transformation from the parent function y = √x to the new equation y - 2 = 2√(x + 3) is a shift of 3 units left and 2 units up, which is achieved by the inside addition, causing a horizontal shift, and the outside addition indicating a vertical shift.
Step-by-step explanation:
To determine the transformation that occurs to the function y = √x to arrive at the new equation y - 2 = 2√(x + 3), let's rewrite the new function to more easily compare it to the parent function.
Adding 2 to both sides of the new equation gives us y = 2√(x + 3) + 2. Now, we compare this to the parent function y = √x.
The √(x + 3) indicates a horizontal shift, and because it is (x + 3), the shift is 3 units to the left of the coordinate system (since adding inside the function moves in the opposite direction). The multiplication of the square root part by 2 indicates that there is vertical stretching by a factor of 2, but this doesn't involve a shift in position, so we won't focus on it. The +2 at the end of the equation indicates a vertical shift upwards by 2 units in the coordinate system.
Therefore, the correct transformation is a shift of 3 units left and 2 units up, which corresponds to option (c): Shift 2 units up and 3 units left.