Question

what transformation should be applied to the graph of $f(x) = \sin x$ so that its midline is changed to $y = -2$? (1 point)\
\bigcirc translate 1 unit down.\
\bigcirc translate 2 units up.\
\bigcirc translate 2 units down.\
\bigcirc translate 3 units down.

Explanation:

Step1: Recall the midline of \(y = \sin x\)

The mid - line of \(y=\sin x\) is \(y = 0\).

Step2: Determine the vertical translation

We want to change the mid - line from \(y = 0\) to \(y=-2\).
The formula for a vertical translation of a function \(y = f(x)\) is \(y=f(x)+k\), where \(k\) is the vertical shift.
If \(y=\sin x + k\), and we want the mid - line \(y=-2\), then when \(\sin x = 0\) (at mid - line points), \(y=k\). So \(k=-2\).
A vertical shift of \(k=-2\) means the graph is translated \(2\) units down.

Answer:

Translate 2 units down.