Question

The function $f\left(x\right)=3\sin \left(4x\right)$has amplitude _____ and period _______.

Short answer

The function $f\left(x\right)=3\sin \left(4x\right)$has amplitude$3$and period$\frac{\mathrm{\pi }}{2}$.

Step-by-step solution

Step 1. Given information.

We have:

$f\left(x\right)=3\sin \left(4x\right)$

Step 2. Fill the blank.

The function is $f\left(x\right)=3\sin \left(4x\right)$.

Use the form $f\left(x\right)=a\sin (bx-c)+d$, where $a$is amplitude.

$$\begin{gathered} A=\left|a\right| \\ =\left|3\right| \\ =3 \\ \text{Period=}\frac{\mathrm{\pi }}{2} \end{gathered}$$