Choose the graph which matches the function.
-$$f ( x ) = 3 ^ { - x } \cos 4 x$$
A) Damping factor $= 4$, damping occurs as $x \rightarrow \infty$
B) Damping factor $= 3 ^ { - x }$, damping occurs as $x \rightarrow 0$
C) Damping factor $= 3 ^ { - x }$, damping occurs as $\mathrm { x } \rightarrow \infty$.
D) No damping

Question

Quizplus · Accepted Answer

The function $f(x) = 3^{-x} \cos 4x$ has a damping factor of $3^{-x}$, which means the amplitude of the cosine wave decreases as $x$ increases. This is because $3^{-x}$ approaches 0 as $x$ approaches infinity, causing the overall function to approach 0 in amplitude, hence the correct choice is the one that states the damping factor is $3^{-x}$ and that damping occurs as $x \rightarrow \infty$.

Choose the Graph Which Matches the Function f(x)=3−xcos⁡4xf ( x ) = 3 ^ { - x } \cos 4 xf(x)=3−xcos4x

Choose the Graph Which Matches the Function $f ( x ) = 3 ^ { - x } \cos 4 x$