Answer
$\color{blue}{y=-\sin{x}+1}$ or $\color{blue}{y=1-\sin{x}}$
Work Step by Step
The y-values vary from $0$ to $2$.
This means that the amplitude is $\frac{2}{2}=1$.
The given graph is a reflection of a sine function. so $a$ must be negative.
Since the amplitude is $|a|$ and $a$ is negative, then $a=-1$.
Thus, the tentative equation of the function whose graph is given is $y=-1\sin{(bx)}\longrightarrow y=-\sin{(bx)}$.
The period of a sine function is $\frac{2\pi}{b}$.
Since the period of the given function is $2\pi$, then $b$ must be $1$.
Therefore, the tentative equation of the function whose graph is given is $y=-\sin{x}$.
Recall that when $|a|=1$, the y-values of $y=a \cdot \sin{(bx)}$ vary from $-1$ to $1$.
Since the y-values of the given graph vary from $0$ to $2$, then it means that $1$ is being added to each y-value of the parent function $y=\sin{x}$.
Therefore, the equation of the function whose graph is given is: $\color{blue}{y=-\sin{x}+1}$ or $\color{blue}{y=1-\sin{x}}$
