If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi/3), what should be used for Xmin and Xmax? Explain your answer.

P.S. "It only wants the first and last numbers for the domain."

Question

If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x - pi/3), what should be used for Xmin and Xmax? Explain your answer.

P.S. "It only wants the first and last numbers for the domain."

zehanz · Answer

You want to have two complete periods. The period of cos is 2 pi.
The period of this function is pi, because of the 2 before x.
So two periods will fit in the interval [0, 2pi].

If you want the graph to begin with the "normal" starting point of the cos-function, you need to do a bit of extra reasoning: The graph is translated pi/3 to the right, so you also could take as domain: [pi/3, 7pi/3].