Main Answer:The given periodic function f(t) is given by the function, Where,f(t) = 2[2 + 2. (3t for 0 ≤ t < 1/3f(t) = 2[2 - 2. (3t for 1/3 ≤ t < 2/3f(t) = 2[2 + 2. (3t - 2 for 2/3 ≤ t < 1The graph of the given periodic function is shown below:Answer more than 100 words:A periodic function is defined as a function that repeats its values after a regular interval of time. The most basic example of a periodic function is the trigonometric function, such as the sine and cosine functions.In the given question, we are given a periodic function f(t), which is defined as follows:f(t) = 2[2 + 2. (3t for 0 ≤ t < 1/3f(t) = 2[2 - 2. (3t for 1/3 ≤ t < 2/3f(t) = 2[2 + 2. (3t - 2 for 2/3 ≤ t < 1We can see that the given function is divided into three parts. For 0 ≤ t < 1/3, the function is an increasing linear function of t. For 1/3 ≤ t < 2/3, the function is a decreasing linear function of t. For 2/3 ≤ t < 1, the function is an increasing linear function of t, but it is shifted downwards by 2 units.We can plot the graph of the given periodic function by plotting the individual graphs of each part of the function. The graph of the given periodic function is shown below:Conclusion:In conclusion, we can say that the given function is a periodic function, which repeats its values after a regular interval of time. The function is divided into three parts, and each part is a linear function of t. The graph of the given periodic function is shown above.