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 divided by three), what should be used for xmin and xmax? explain your answer.

The correct given equation is:

y = 5 + 3 cos 2 (x – π/3)

 To answer this problem, we must remember that:

y = A cos [w(x - π)], the period is 2 π / w and the phase shift is π (the beginning of one period)

Rewriting the given equation to this form,

y = 5 + 3cos [2(x - π/3)] 

Therefore,

period = 2 π / 2 = π
phase shift = π /3 

So to create two periods, you need an interval of 2 π
If you start at π /3, you'll start and end at the max of the cos function.

Therefore,

 [Xmin , Xmax] = [π /3 , 7 π /3] would create a complete graph of 2 periods.

ANSWER: [π /3 , 7 π /3]

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.