Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$f ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln x$
A) Reflect across the $x$-axis and the $y$-axis and translate5 units down.
B) Reflect across the $y$-axis and vertically stretch by a factor of 5 .
C) Reflect across the $x$-axis and translate 5 units down.
D) Reflect across the $x$-axis and the $y$-axis and vertically stretch by a factor of 5 .

Question

Quizplus · Accepted Answer

The transformation involves a reflection across the $y$-axis due to the negative sign inside the logarithm function (changing $x$ to $-x$), a reflection across the $x$-axis because of the negative sign outside the logarithm function, and a vertical stretch by a factor of 5 due to the multiplication by 5.

Describe How to Transform the Graph of the Basic Function f(x)=−5ln⁡(−x);g(x)=ln⁡xf ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln xf(x)=−5ln(−x);g(x)=lnx

Describe How to Transform the Graph of the Basic Function $f ( x ) = - 5 \ln ( - x ) ; \quad g ( x ) = \ln x$