Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = - 6 \cos 3 x ; g ( x ) = \cos x$$
A) Horizontal shrink by a factor $\frac { 1 } { 6 }$, vertical stretch by a factor of 3 , reflection across $y$-axis
B) Horizontal stretch by a factor 3 , vertical stretch by a factor of 6 , reflection across $x$-axis
C) Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $\mathrm { y }$-axis
D) Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 6 , reflection across $x$-axis

Question

Quizplus · Accepted Answer

The transformation from $g(x) = \cos x$ to $f(x) = -6\cos 3x$ involves a horizontal shrink by a factor of $\frac{1}{3}$ (because of the $3x$, which compresses the period of the cosine function), a vertical stretch by a factor of 6 (due to the coefficient $-6$), and a reflection across the $x$-axis (indicated by the negative sign in front of the 6).

Describe the Transformations Required to Obtain the Graph of the Function