Answer
$a=2$, $b=1$ and $c=-\frac{\pi}{4}$
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 $2\pi$:
$$period=\frac{2\pi}{b}$$ $$b=\frac{2\pi}{period}=\frac{2\pi}{2\pi}=1$$
From the graph, the shift is $\frac{\pi}{4}$ to the left or $-\frac{\pi}{4}$:
$$\frac{c}{b}=-\frac{\pi}{4}$$ $$c=-\frac{\pi}{4}b=-\frac{\pi}{4}(1)=-\frac{\pi}{4}$$
Thus, $a=2$, $b=1$ and $c=-\frac{\pi}{4}$.
