Answer:
See explanation
Step-by-step explanation:
A. The graph of the function [tex]f(x)=3-\sin \dfrac{\pi x}{3}[/tex] is shown in attached diagram.
B. The period of the function [tex]f(x)=3-\sin \dfrac{\pi x}{3}[/tex] is
[tex]T=\dfrac{2\pi}{\frac{\pi}{3}}=6.[/tex]
C. The values of [tex]\sin \dfrac{\pi x}{3}[/tex] are [tex][-1,1],[/tex] so the maximum value of the function [tex]f(x)=3-\sin \dfrac{\pi x}{3}[/tex] is
[tex]3-(-1)=4.[/tex]
D. The smallest positive x for which f(x) is maximum is x=4.5 (black point on the graph).
