Choose the graph which matches the function.
-$f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } \sin 3 x$
A) Damping factor $= 3$, damping occurs as $x \rightarrow 0$
B) Damping factor $= \left( \frac { 1 } { 2 } \right) ^ { x }$, damping occurs as $x \rightarrow \infty$
C) No damping
D) Damping factor $= \left( \frac { 1 } { 2 } \right) ^ { x }$, damping occurs as $x \rightarrow 0$

Question

Quizplus · Accepted Answer

The function $f(x) = \left( \frac{1}{2} \right)^x \sin 3x$ has a damping factor of $\left( \frac{1}{2} \right)^x$, which means the amplitude of the sine wave decreases as $x$ increases. This results in damping as $x \rightarrow \infty$, not as $x \rightarrow 0$.

Choose the Graph Which Matches the Function f(x)=(12)xsin⁡3xf ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } \sin 3 xf(x)=(21​)xsin3x

Choose the Graph Which Matches the Function $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x } \sin 3 x$