Describe how to transform the graph of f into the graph of g.
-$f ( x ) = \sqrt { x }$ and $g ( x ) = - \sqrt { x + 4 }$
A) Shift the graph of $f$ right 4 units and then reflect across the $x$-axis.
B) Shift the graph of $f$ left 4 units and then reflect across the $x$-axis.
C) Shift the graph of $f$ left 4 units and then reflect across the $y$-axis.
D) Shift the graph of $f$ up 4 units and then reflect across the $y$-axis.

Question

Quizplus · Accepted Answer

The transformation from $f(x) = \sqrt{x}$ to $g(x) = -\sqrt{x + 4}$ involves two steps. First, adding 4 inside the square root shifts the graph 4 units to the left, not to the right, because it's in the form of $x + a$, where $a = 4$. Second, the negative sign in front of the square root reflects the graph across the $x$-axis. Therefore, the correct transformation is to shift the graph of $f$ left 4 units and then reflect it across the $x$-axis.

Describe How to Transform the Graph of F into the Graph