Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x).
-$$f ( x ) = 2 \log ( 4 - x ) ; \quad g ( x ) = \log x$$
A) Reflect across the $y$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 .
B) Reflect across the $y$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 .
C) Reflect across the $x$-axis, translate 4 units to the left, and vertically stretch by a factor of 2 .
D) Reflect across the $x$-axis, translate 4 units to the right, and vertically stretch by a factor of 2 .

Question

Quizplus · Accepted Answer

The function $f(x) = 2 \log(4 - x)$ can be obtained from $g(x) = \log x$ by reflecting across the $y$-axis (due to the $-x$), translating 4 units to the right (due to the $4 - x$), and vertically stretching by a factor of 2 (due to the coefficient 2).

Describe How to Transform the Graph of the Basic Function f(x)=2log⁡(4−x);g(x)=log⁡xf ( x ) = 2 \log ( 4 - x ) ; \quad g ( x ) = \log xf(x)=2log(4−x);g(x)=logx

Describe How to Transform the Graph of the Basic Function $f ( x ) = 2 \log ( 4 - x ) ; \quad g ( x ) = \log x$