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22-23 Precalculus Final Part 1
Question 1-3
In Tau Lake, the water level rises and falls over a consistent period of time. The water typically attains its highot level at "high tide" occurs at $5 \mathrm{am}$, the water level is $8 "$ above sea level. Six hours later, at low tide, the water level is 2" above sea level. Which of the fo level as a function of time after midnight?
$f(x)=3 \sin \left(\frac{\pi}{6}(x-2)\right)+5$
$f(x)=3 \cos \left(\frac{\pi}{6}(x-2)\right)+5$
$f(x)=5 \sin \left(\frac{\pi}{6}(x-2)\right)+3$
$f(x)=5 \cos \left(\frac{\pi}{6}(x-2)\right)+3$
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Answer
\( \boxed{f(x)=3 \sin \left(\frac{\pi}{6}(x-2)\right)+5} \)
Step 1 ：Test each function at x = 5 and x = 11
Step 2 ：Only the first function gives the correct water levels at 5 am (8") and 11 am (2")
Step 3 ：\( \boxed{f(x)=3 \sin \left(\frac{\pi}{6}(x-2)\right)+5} \)
