HELLLPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!! 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.

Question

phi · Answer

you have to find the period, so you know how big x has to be to go 2 periods.
I think you can always start at Xmin=0.

anonymous · Answer

Is this the period 2pi / 2 = pi? @phi

phi · Answer

yes

anonymous · Answer

So now what is the next step?

phi · Answer

I guess you graph 2 periods of the function, from say 0 to 2pi
use a graphing calculator, or just evaluate a few points and connect the dots.

anonymous · Answer

Okay would this be a good explation: The period is 2pi / 2 = pi and the phase shift is pi/3
so for two periods, you need an interval of 2pi. if you start at pi/3, you'll start and end at the max of the cos function. So [Xmin , Xmax] of [pi/3 , 7pi/3] would start at the phase shift, but any interval of 2pi will include 2 complete cycles.

anonymous · Answer

Thank you @phi