Answer:
[tex]y=\sqrt{9x+45}+2\\\\\implies y=\sqrt{9(x+5)}+2\\\\\implies y=3\sqrt{x+5}+ 2 [/tex]
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
[tex]\implies y = 3\sqrt{x+5}[/tex]
Next, The graph is shifted up by 2 units
[tex]\implies y = 3\sqrt{x+5}+2[/tex]
Thus, By doing the above translations we can get the required graph.
The resultant graph is attached below :
