For the function $f(x)=2 \cot x$ determine its stretching factor and phase shift, and then graph it for two periods.
Enter the exact answers.
Stretching factor $=$
Phase shift:
no phase shift
Using your answers for the stretching factor and phase shift, select the correct graph of the function $f(x)=2 \cot x$

Step 1 ：Since the function is given by $f(x) = 2 \cot x$, there is no phase shift, as there is no addition or subtraction inside the cotangent function.

Step 2 ：The stretching factor is the coefficient of the cotangent function, which is $2$. So, the stretching factor is $\boxed{2}$.

Step 3 ：To graph the function for two periods, we can first graph the basic cotangent function $y = \cot x$ and then apply the stretching factor.

Step 4 ：The period of the cotangent function is $\pi$, so we can graph it from $0$ to $2\pi$ for one period and from $2\pi$ to $4\pi$ for the second period.

Step 5 ：Now, we apply the stretching factor of $2$ by multiplying the cotangent function by $2$. This will stretch the graph vertically.

Step 6 ：Finally, we can plot the graph of $y = 2 \cot x$ for two periods.