Question

describe how the graph of
y = sin x
can be transformed into the graph of
$y = \frac{1}{7} \sin x$.
options: compress vertically, compress horizontally, no dilations have been made, stretch vertically

Explanation:

To determine the transformation from \( y = \sin x \) to \( y=\frac{1}{7}\sin x \), we use the concept of vertical dilations (stretching or compressing) of a function. For a function \( y = A\sin x \), the value of \( |A| \) determines vertical transformation:

• If \( 0 < |A| < 1 \), the graph is vertically compressed by a factor of \( \frac{1}{|A|} \) (or equivalently, compressed vertically by the factor \( |A| \) in terms of the multiplier).
• If \( |A|>1 \), the graph is vertically stretched.

Here, \( A=\frac{1}{7} \), and \( 0<\frac{1}{7}<1 \). So the graph of \( y = \sin x \) is vertically compressed by a factor (since multiplying the function by a number between 0 and 1 compresses it vertically) to get \( y=\frac{1}{7}\sin x \).

Answer:

A. Compress vertically