Answer:
The correct option is:
The graph of g(x) is the graph of f(x) translated 7 units up and 7 units right.
Option A is correct option.
Step-by-step explanation:
The parent function is: [tex]f(x)=\sqrt{x}[/tex]
The transformed function is: [tex]g(x)=\sqrt{x-7} +7[/tex]
We need to find the statement that best describes the transformed function.
We know the transformation rule:
If f(x) is transformed into f(x)+c, then the function is transformed vertically c units up.
If f(x) is transformed into f(x)-c, then the function is transformed vertically c units down.
If f(x) is transformed into f(x-c) then the function is transformed right c units.
If f(x) is transformed into f(x+c) then the function is transformed left c units.
So, In the given transformation:
The parent function is: [tex]f(x)=x^2[/tex]
The transformed function is: [tex]g(x)=\sqrt{x-7} +7[/tex]
The transformed function is shifted 7 units up [tex]g(x)=\sqrt{x-7} \mathbf{ +7}[/tex] and 7 units right [tex]g(x)=\sqrt{x\mathbf{-7}} +7[/tex]
So, The correct option is:
The graph of g(x) is the graph of f(x) translated 7 units up and 7 units right.
Option A is correct option.
