Answer
$a=2$, $b=\frac{\pi}{2}$ and $c=\frac{\pi}{2}$
Work Step by Step
From the graph, the amplitude is $2$. Consider the positive value, $a=2$.
Rewriting the function $f(x)=a\sin b\left(x-\frac{c}{b}\right)$ and from the graph, the period is $4$:
$$period=\frac{2\pi}{b}$$ $$b=\frac{2\pi}{period}=\frac{2\pi}{4}=\frac{\pi}{2}$$
From the graph, the shift is $1$ to the right:
$$\frac{c}{b}=1$$ $$c=1b=1\left(\frac{\pi}{2}\right)=\frac{\pi}{2}$$
Thus, $a=2$, $b=\frac{\pi}{2}$ and $c=\frac{\pi}{2}$.
