Use the graph of the parent function, f left-parenthesis x right-parenthesis equals Start Root x End Root, to describe the transformation for the graph of g left-parenthesis x right-parenthesis equals Start Root x minus 5 End Root.

Question

(1 point)
Responses

The graph of g left-parenthesis x right-parenthesis is the graph of f left-parenthesis x right-parenthesis shifted up 5 units.
The graph of Image with alt text: g left-parenthesis x right-parenthesis is the graph of Image with alt text: f left-parenthesis x right-parenthesis shifted up 5 units.

The graph of g left-parenthesis x right-parenthesis is the graph of f left-parenthesis x right-parenthesis shifted down 5 units.
The graph of Image with alt text: g left-parenthesis x right-parenthesis is the graph of Image with alt text: f left-parenthesis x right-parenthesis shifted down 5 units.

The graph of g left-parenthesis x right-parenthesis is the graph of f left-parenthesis x right-parenthesis shifted right 5 units.
The graph of Image with alt text: g left-parenthesis x right-parenthesis is the graph of Image with alt text: f left-parenthesis x right-parenthesis shifted right 5 units.

The graph of g left-parenthesis x right-parenthesis is the graph of f left-parenthesis x right-parenthesis shifted left 5 units.

Answer 1

To analyze the transformation from the parent function \( f(x) = \sqrt{x} \) to the function \( g(x) = \sqrt{x - 5} \), we can focus on the argument of the square root function.

The transformation can be described as follows:

• The term \( x - 5 \) inside the square root indicates a horizontal shift of the graph. Specifically, when you have \( f(x - h) \), where \( h \) is positive, the graph shifts to the right by \( h \) units.

In this case, since \( g(x) = \sqrt{x - 5} \):

• The graph of \( g(x) \) is the graph of \( f(x) \) shifted right by 5 units.

Therefore, the correct response is:

The graph of \( g(x) \) is the graph of \( f(x) \) shifted right 5 units.