consider the graph of the sine function. each grid line on the coordinate plane represents 1 unit. which…

Explanation:

Step1: Recall the general form of sine - function

The general form of a sine - function is $y = A\sin(x)+k$, where $A$ is the amplitude and $k$ is the vertical shift.

Step2: Determine the amplitude

The amplitude of a sine - function is half of the vertical distance between the maximum and minimum values. Looking at the graph, if we assume the normal sine - function range is from $- 1$ to $1$, and we observe the vertical distance between the maximum and minimum values of the given graph. The distance between the maximum and minimum values of the graph is $4$ units. So, the amplitude $A=\frac{4}{2}=2$.

Step3: Determine the vertical shift

The mid - line of the normal sine function $y = \sin(x)$ is $y = 0$. For the given graph, the mid - line is at $y=-2$. So, the vertical shift $k=-2$.

Step4: Write the function

The function of the form $y = A\sin(x)+k$ with $A = 2$ and $k=-2$ is $f(x)=2\sin(x)-2$.

Answer:

$f(x)=2\cdot\sin(x)-2$