Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.5 Write Trigonometric Functions and Models - 14.5 Exercises - Quiz for Lessons 14.3-14.5 - Page 945: 10

$y =3 \sin \pi x-2$

The general solution for the trigonometric functions $sine$ and $cosine$ is as follows: $y=A \sin B (x-h) +k $ and $y=A \cos B (x-h)+k$ Amplitude, $|a|= \dfrac{M-m}{2}= \dfrac{1-(-5)}{2}= 3$ Vertical Shift, $k= \dfrac{M+m}{2}= \dfrac{1+(-5)}{2}=-2$ Since the time period for the trigonometric function $\sin $ is $\pi$: We have $y =3 \sin \pi x-2$