Question

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

Explanation:

Step1: Rewrite the second equation

Start with the equation \(2y=\sin x\). We can solve for \(y\) by dividing both sides by 2. This gives us \(y = \frac{1}{2}\sin x\).

Step2: Compare with the original function

The original function is \(y=\sin x\). The transformed function is \(y=\frac{1}{2}\sin x\). For a function of the form \(y = A\sin x\), when \(|A|< 1\), it represents a vertical compression of the graph of \(y = \sin x\) by a factor of \(|A|\). Here, \(A=\frac{1}{2}\), so the graph of \(y = \sin x\) is vertically compressed by a factor of \(\frac{1}{2}\) (or equivalently, we can say it is vertically compressed) to get the graph of \(y=\frac{1}{2}\sin x\) (which is the same as the graph of \(2y=\sin x\) after solving for \(y\)).

Answer:

Compress vertically