Final answer:
The graph of y = √(x) will be translated to the right by 3 units and up by 1 unit to become y = √(x-3) + 1. The new translated graph starts at point (3,1).
Step-by-step explanation:
The graph of the function y = √(x) after the translation (x, y) → (x-3, y+1) results in moving all points on the original graph 3 units to the right and 1 unit up. This means that if you have a point (a, b) on the graph of y = √(x), it would now be located at (a+3, b+1) on the translated graph. The new equation representing the translated graph would then be y = √(x-3) + 1.
To visualize the translation on a coordinate plane, you begin by sketching the original graph of y = √(x), which starts at the origin (0,0) and extends to the right since the square root function is only defined for non-negative values of x. Then, you shift every point on this graph to the right by 3 units and up by 1 unit to obtain the translated graph. The graphical representation will now start at the point (3,1) instead of the origin.