Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$$
A) Translate 2 units to the left and 5 units up.
B) Translate 5 units to the left and 2 units down.
C) Translate 2 units to the right and 5 units down.
D) Translate 2 units to the right and 5 units up.

Question

Quizplus · Accepted Answer

The function $f(x) = \ln(x - 2) + 5$ is obtained from $g(x) = \ln x$ by first translating the graph 2 units to the right (to account for the $x - 2$ inside the logarithm, which shifts the graph to the right by 2 units) and then translating it 5 units up (to account for the $+ 5$ outside the logarithm, which shifts the graph upwards by 5 units).

Describe How to Transform the Graph of the Basic Function f(x)=ln⁡(x−2)+5;g(x)=ln⁡xf ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln xf(x)=ln(x−2)+5;g(x)=lnx

Describe How to Transform the Graph of the Basic Function $f ( x ) = \ln ( x - 2 ) + 5 ; \quad g ( x ) = \ln x$