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artcher [175]
4 years ago
7

Given f(x) = 3 - sin(πx/3)

Mathematics
1 answer:
Cerrena [4.2K]4 years ago
8 0

Answer:

See explanation

Step-by-step explanation:

A. The graph of the function f(x)=3-\sin \dfrac{\pi x}{3} is shown in attached diagram.

B. The period of the function f(x)=3-\sin \dfrac{\pi x}{3} is

T=\dfrac{2\pi}{\frac{\pi}{3}}=6.

C. The values of \sin \dfrac{\pi x}{3} are [-1,1], so the maximum value of the function f(x)=3-\sin \dfrac{\pi x}{3} is

3-(-1)=4.

D. The smallest positive x for which f(x) is maximum is x=4.5 (black point on the graph).

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