Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. $$f ( x ) = 3 e ^ { - x } \cos x$$
A)
B)
C)
D)

Question

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $$f ( x ) = 3 e ^ { - x } \cos x$$ ​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

The graph in choice D resembles a damped sinusoidal function, which is the type of function described in the problem. Additionally, the damping factor can be identified by examining the exponential decay of the amplitude of the function over time. In choice D, the amplitude decays slightly with each oscillation, indicating a damping factor of less than 1. Choices A, B, C, and E do not exhibit the same type of decay in amplitude and therefore do not accurately represent the given function.

Use a Graphing Utility to Select the Graph of the Function