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Unformatted text preview: Solution: We model the function H ( t ) as a sinusoidal function. The graph below shows temperature ( H ) as a function of the time t in hours. This is a phase-shifted cosine function with amplitude 15 and period 24. There is also a vertical shift of 85 units up. Since the period = 2 B , we see that B = 12 . H ( t ) = 85 + 15 cos 12 ( t-12) 4. Draw a graph of the function f ( x ) = arctan x . Label all important behavior. 2 5. Find a possible formula for the function g ( x ) whose graph is given below. Solution: Notice that there are three roots (zeros) of g ( x ): -3, 0, and 4. Hence, g ( x ) = k ( x + 3) x ( x-4) for some constant k . We can determine k by using the fact that (2 , 3) is on the graph: 3 = g (2) = k (2 + 3)(2)(2-4) 3 =-20 k k = 3-20 Hence, g ( x ) =-3 20 ( x + 3) x ( x-4) 3...
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