Find the function that is finally graphed after the following transformations are applied to the graph of $y=\sqrt{x}$ in the order listed.
(1) Vertical stretch by a factor of 4
(2) Shift up 1 unit
(3) Shift left 3 units

Step 1 ：The transformations applied to the function \(y=\sqrt{x}\) are as follows:

Step 2 ：1) Vertical stretch by a factor of 4: This means we multiply the output of the function by 4. So, \(y=\sqrt{x}\) becomes \(y=4\sqrt{x}\).

Step 3 ：2) Shift up 1 unit: This means we add 1 to the output of the function. So, \(y=4\sqrt{x}\) becomes \(y=4\sqrt{x}+1\).

Step 4 ：3) Shift left 3 units: This means we replace \(x\) with \(x+3\) in the function. So, \(y=4\sqrt{x}+1\) becomes \(y=4\sqrt{x+3}+1\).

Step 5 ：Final Answer: The function that is finally graphed after the transformations are applied to the graph of \(y=\sqrt{x}\) is \(\boxed{y=4\sqrt{x+3}+1}\). The graph of this function is a curve that starts from the point (0,7.93) and increases as x increases. The transformations have the effect of stretching the graph vertically by a factor of 4, shifting it up by 1 unit, and shifting it left by 3 units.