Answer
$y= 4 -\cos 3x$
Work Step by Step
General solution for Trigonometric functions $sine$ and $cosine$ that model a sinusoid is as follows: $y=A \sin B (x-h) +k $ and $y=A \cos B (x-h)+k$
Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{5-3}{2}= \dfrac{2}{2}$
Thus, we have $|a|=1$
Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{5+3}{2}$
This gives: $|k|=\dfrac{8}{2}=4$
Therefore, the period is: $P=2( \dfrac{\pi}{3}-0) =\dfrac{2 \pi}{3}$
and $\dfrac{2 \pi}{a}=\dfrac{2 \pi}{3} \implies a=3$
Hence, the function is: $y= 4 -\cos 3x$
