Answer:
\(y=\sqrt{9x+45}+2\\\\\implies y=\sqrt{9(x+5)}+2\\\\\implies y=3\sqrt{x+5}+ 2\)
Now, Take the graph of the parent function as y = √x
Then dilate it by 3 units
⇒ y = 3√x
Next, the resultant graph is shifted 5 units to the left
\(\implies y = 3\sqrt{x+5}\)
Next, The graph is shifted up by 2 units
\(\implies y = 3\sqrt{x+5}+2\)
Thus, By doing the above translations we can get the required graph.
The resultant graph is attached below :
