Question

use transformations of ( f(x) = sqrt{x} ) to graph the following function. ( g(x) = sqrt{x} - 2 ) what transformation is needed to graph the function ( g(x) = sqrt{x} - 2 )? choose the correct answer below. a. the graph of ( f(x) = sqrt{x} ) should be shifted 2 units down. b. the graph of ( f(x) = sqrt{x} ) should be shifted 2 units to the right. c. the graph of ( f(x) = sqrt{x} ) should be shifted 2 units up. d. the graph of ( f(x) = sqrt{x} ) should be shifted 2 units to the left.

Explanation:

For a parent function $f(x)$, the transformation $f(x) - k$ (where $k>0$) shifts the graph of $f(x)$ downward by $k$ units. Here, $g(x) = f(x) - 2$ with $f(x)=\sqrt{x}$, so the graph shifts down 2 units.

Answer:

A. The graph of $f(x)=\sqrt{x}$ should be shifted 2 units down.