6. $y = -3cos(\frac{1}{3}x)-1$

Explanation:

Step1: Identify the amplitude

The general form of a cosine function is $y = A\cos(Bx - C)+D$. For the function $y=-3\cos(\frac{1}{3}x)-1$, the amplitude $|A|$. Here $A = - 3$, so the amplitude is $| - 3|=3$.

Step2: Identify the period

The period of a cosine function $y = A\cos(Bx - C)+D$ is given by $T=\frac{2\pi}{|B|}$. Here $B=\frac{1}{3}$, so $T=\frac{2\pi}{\left|\frac{1}{3}\right|}=6\pi$.

Step3: Identify the vertical shift

The vertical - shift of the function $y = A\cos(Bx - C)+D$ is $D$. Here $D=-1$, so the graph is shifted 1 unit down.

Step4: Identify the phase shift

The phase shift of the function $y = A\cos(Bx - C)+D$ is $\frac{C}{B}$. Since $C = 0$ and $B=\frac{1}{3}$, the phase shift is $0$.

Answer:

Amplitude: 3; Period: $6\pi$; Vertical shift: 1 unit down; Phase shift: 0