Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( - x ) - 4 ; g ( x ) = \ln x$$
A) Reflect across the $x$-axis and translate 4 units to the left.
B) Reflect across the $y$-axis and translate 4 units down.
C) Reflect across the $y$-axis and translate 4 units to the left.
D) Reflect across the $x$-axis and translate 4 units down.

Question

Quizplus · Accepted Answer

Reflecting $g(x) = \ln x$ across the $y$-axis changes $x$ to $-x$, resulting in $\ln(-x)$. Translating 4 units down involves subtracting 4 from the function, leading to $\ln(-x) - 4$.

Describe How to Transform the Graph of the Basic Function f(x)=ln⁡(−x)−4;g(x)=ln⁡xf ( x ) = \ln ( - x ) - 4 ; g ( x ) = \ln xf(x)=ln(−x)−4;g(x)=lnx

Describe How to Transform the Graph of the Basic Function $f ( x ) = \ln ( - x ) - 4 ; g ( x ) = \ln x$