Describe how to transform the graph of f into the graph of g.
-$$f ( x ) = \sqrt { x } \text { and } g ( x ) = - \sqrt { - x }$$
A) The two graphs are the same.
B) Reflect the graph of $f$ across the $y$-axis.
C) Reflect the graph of $f$ across the $x$-axis.
D) Reflect the graph of $\mathrm { f }$ across the $y$-axis and then reflect across the $x$-axis.

Question

Quizplus · Accepted Answer

To transform $f(x) = \sqrt{x}$ into $g(x) = -\sqrt{-x}$, you first reflect $f$ across the $y$-axis to account for the input change from $x$ to $-x$, which makes the function handle negative inputs instead of positive ones. Then, you reflect across the $x$-axis to account for the negative sign outside the square root, which flips the graph vertically.

Describe How to Transform the Graph of F into the Graph