describe the transformation of the graph of f(x)=sin x + 2 to the graph labeled option 2. (1 point). option…

Explanation:

Step1: Recall transformation rules

The general rules for function transformations are: $-f(x)$ reflects the graph of $y = f(x)$ about the $x -$axis, $f(-x)$ reflects the graph about the $y -$axis, and $f(x - h)$ shifts the graph of $y=f(x)$ to the right by $h$ units.

Step2: Analyze the given function $f(x)=\sin x + 2$ and Option 2

The graph of $y = f(x)=\sin x+2$ has a mid - line at $y = 2$. The graph of Option 2 has a mid - line at $y=-2$. Also, the shape of the sine - wave is inverted. The transformation that inverts the graph of $y = f(x)$ about the $x -$axis is $y=-f(x)$. When $f(x)=\sin x + 2$, then $-f(x)=-\sin x - 2$. This transformation will flip the graph of $y=\sin x + 2$ over the $x -$axis.

Answer:

Option 2 is the graph of $-f(x)$.