Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$$
A) Reflect across the $y$-axis and translate 10 units to the right.
B) Reflect across the $x$-axis and translate 10 units down.
C) Reflect across the $y$-axis and translate 10 units up.
D) Reflect across the $x$-axis and translate 10 units to the right.

Question

Quizplus · Accepted Answer

The transformation involves reflecting the graph of $g(x) = \ln x$ across the $y$-axis to accommodate the negative inside the logarithm ($\ln(-x)$), which changes the domain from $x > 0$ to $x < 0$. Then, adding 10 ($+ 10$) translates the graph 10 units up on the $y$-axis.

Describe How to Transform the Graph of the Basic Function f(x)=ln⁡(−x)+10;g(x)=ln⁡xf ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln xf(x)=ln(−x)+10;g(x)=lnx

Describe How to Transform the Graph of the Basic Function $f ( x ) = \ln ( - x ) + 10 ; g ( x ) = \ln x$