Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Skill Practice - Page 944: 9

$y= 6 \sin \dfrac{x}{2}$

Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{6-(-6)}{2}= \dfrac{12}{2}$ Thus, we have $|a|=6$ Vertical amplitude, $k= \dfrac{M+m}{2}= \dfrac{6+(-6)}{2}$ This gives: $|k|= \dfrac{6-6}{2}=0$ Therefore, the period is: $P=2( 3 \pi-\pi) = 4 \pi$ and $\dfrac{2 \pi}{a}=4 \pi \implies a=\dfrac{1}{2}$ Hence, the function is: $y= 6 \sin \dfrac{x}{2}$