Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( 8 - x ) - 7 ; \quad g ( x ) = \ln x$$
A) Reflect across the $y$-axis and then translate 8 units to the left and 7 units down.
B) Reflect across the $y$-axis and then translate 8 units to the right and 7 units down.
C) Translate 8 units to the right and 7 units down.
D) Reflect across the $x$-axis and then translate 8 units to the left and 7 units down.

Question

Quizplus · Accepted Answer

The transformation from $g(x) = \ln x$ to $f(x) = \ln(8 - x) - 7$ involves reflecting the graph across the $y$-axis (to account for the $-x$ inside the logarithm, which reverses the input values), and then translating it 8 units to the right (to make the inside of the logarithm $8 - x$ instead of $x$) and 7 units down (to subtract 7 from the output values).

Describe How to Transform the Graph of the Basic Function f(x)=ln⁡(8−x)−7;g(x)=ln⁡xf ( x ) = \ln ( 8 - x ) - 7 ; \quad g ( x ) = \ln xf(x)=ln(8−x)−7;g(x)=lnx

Describe How to Transform the Graph of the Basic Function $f ( x ) = \ln ( 8 - x ) - 7 ; \quad g ( x ) = \ln x$