Answer:
The smallest possible domain to completely graph two periods is either [0, 2π] or [-π, π].
Step-by-step explanation:
The period of cosine function [0, 2π].
The given function is
\(y=5+3\cos 2(x-\frac{\pi}{3})\)
This function can be written as
\(y=5+3\cos (2x-\frac{2\pi}{3})\) .... (1)
The general form of cosine function is
\(y=A\cos (Bx+C)+D\) .... (2)
where, A is amplitude, \(\frac{2\pi}{B}\), C is phase and D is midline.
From (1) and (2), we get
\(A=3,B=2C=\frac{2\pi}{3},D=5\)
\(Period=\frac{2\pi}{2}=\pi\)
The period of given function is [0,π]. So, the smallest possible domain to completely graph two periods is either [0, 2π] or [-π, π].
