Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = \frac { 1 } { 5 } \sin \frac { 3 x } { 5 } ; g ( x ) = \sin x$$
A) Horizontal stretch by a factor of 5 , vertical shrink by a factor of $\frac { 3 } { 5 }$
B) Horizontal stretch by a factor of $\frac { 5 } { 3 }$, vertical stretch by a factor of 5
C) Horizontal stretch by a factor of $\frac { 5 } { 3 }$, vertical shrink by a factor of $\frac { 1 } { 5 }$
D) Horizontal shrink by a factor of $\frac { 3 } { 5 }$, vertical shrink by a factor of $\frac { 1 } { 5 }$

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{1}{5}\sin\frac{3x}{5}$ compared to $g(x) = \sin x$ involves a horizontal stretch by a factor of $\frac{5}{3}$ (since the coefficient of $x$ inside the sine function is $\frac{3}{5}$, which inversely affects the period) and a vertical shrink by a factor of $\frac{1}{5}$ (due to the coefficient $\frac{1}{5}$ outside the sine function).

Describe the Transformations Required to Obtain the Graph of the Function