## Precalculus (6th Edition) Blitzer

$y=3cos(\frac{\pi}{6}x)+9$
Step 1. Use the model function $y=AcosBx+D$ with the given information and graph. Step 2. We can identify the average value as $y=9$ which means that $D=9$ Step 3. We can identify the amplitude as $y=\frac{12-6}{2}=3$ and thus $A=3$ Step 4. The period can be found as $p=18-6=12$, thus $\frac{2\pi}{B}=12$ and $B=\frac{\pi}{6}$ Step 5. The model function can be written as $y=3cos(\frac{\pi}{6}x)+9$