The function is stretched vertically by a factor of 3.
The function shifts 2 to the right.
The function is moved 5 units up.
Explanation:
The parent function of the graph is [tex]f(x)=\sqrt{x}[/tex]
The transformation for the parent function is given by [tex]g(x)=3\sqrt{x-2} +5[/tex]
Thus, the transformed function is in the form of [tex]y=a\sqrt{x-h} +k[/tex]
where a is the vertical compression/stretch,
h moves graph to left or right and
k moves the graph up or down.
Thus, from the transformed function [tex]g(x)=3\sqrt{x-2} +5[/tex], we have,
[tex]a=3, h=2 , k=5[/tex]
The attached graph below shows the transformation of the graph that the graph is stretched vertically by a factor of 3 and shifted 2 units to the right and moved 5 units up.
Hence, The function is stretched vertically by a factor of 3.
The function shifts 2 to the right.
The function is moved 5 units up.
