Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = 2 \cos 3 \pi x ; g ( x ) = \cos \pi x$$
A) Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical stretch by a factor of 2
B) Horizontal shrink by a factor $\frac { 1 } { 3 }$, vertical shrink by a factor of $\frac { 1 } { 2 }$
C) Horizontal stretch by a factor 3 , vertical stretch by a factor of 2
D) Horizontal shrink by a factor $\frac { 1 } { 2 }$, vertical stretch by a factor of 3

Question

Quizplus · Accepted Answer

The function $f(x) = 2\cos(3\pi x)$ compared to $g(x) = \cos(\pi x)$ involves a vertical stretch by a factor of 2 due to the coefficient 2, and a horizontal shrink by a factor of $\frac{1}{3}$ because the coefficient inside the cosine function changes from $\pi$ to $3\pi$, which compresses the period of the cosine function by a factor of $\frac{1}{3}$.

Describe the Transformations Required to Obtain the Graph of the Function