Question

Given f(x) = 3 - sin(πx/3)

Answer 1

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).