Question

describe how the graph of y = sin x can be transformed into the graph of y = sin (2x). compress horizontally no dilations have been made stretch horizontally compress vertically

Explanation:

For a function \( y = \sin(Bx) \), the horizontal transformation is determined by the value of \( B \). If \( |B|>1 \), the graph of \( y=\sin x \) is horizontally compressed by a factor of \( \frac{1}{|B|} \). Here, \( B = 2>1 \), so the graph of \( y = \sin x \) is horizontally compressed to get \( y=\sin(2x) \). The other options are incorrect: "No dilations" is wrong as there is a horizontal dilation; "Stretch horizontally" would occur if \( 0<|B|<1 \); "Compress vertically" is about the vertical coefficient (not present here as the vertical coefficient is 1 for both functions).

Answer:

A. Compress horizontally