Answer: Range \(-5\leq f(x)\leq 1\); \(a=3\), \(b=\frac34\), \(c=-2\).

The graph represents a function because each value of \(x\) in the domain has exactly one corresponding value of \(y\).

From the graph, the maximum value is \(1\) and the minimum value is \(-5\). Hence the range is

\(\boxed{-5\leq f(x)\leq 1}.\)

The midline is halfway between the maximum and minimum values:

\(c=\frac{1+(-5)}{2}=-2.\)

The amplitude is

\(|a|=\frac{1-(-5)}{2}=3.\)

Since the graph starts at a maximum, \(a\) is positive, so

\(a=3.\)

One complete cycle runs from \(x=0\) to \(x=\frac{8\pi}{3}\), so the period is

\(\frac{8\pi}{3}.\)

For \(\cos bx\), the period is \(\frac{2\pi}{b}\). Therefore

\(\frac{2\pi}{b}=\frac{8\pi}{3}.\)

So

\(b=\frac34.\)

Thus

\(\boxed{a=3,\quad b=\frac34,\quad c=-2}.\)