graph the following function over the interval -2π, 2π. give the amplitude. y = -4sin x

Explanation:

Step1: Recall amplitude formula

For a sine - function of the form $y = A\sin(x)$, the amplitude is given by $|A|$.

Step2: Identify the value of A

In the function $y=-4\sin(x)$, $A = - 4$.

Step3: Calculate the amplitude

The amplitude is $| - 4|=4$.

To graph the function $y = - 4\sin(x)$ over the interval $[-2\pi,2\pi]$:

1. The standard sine - function $y=\sin(x)$ has a period of $2\pi$. The function $y = - 4\sin(x)$ also has a period of $2\pi$.
2. The key points of the sine - function $y=\sin(x)$ are:
   • When $x = 0$, $y=\sin(0)=0$; for $y=-4\sin(x)$, $y = 0$.
   • When $x=\frac{\pi}{2}$, $y=\sin(\frac{\pi}{2}) = 1$; for $y=-4\sin(x)$, $y=-4$.
   • When $x=\pi$, $y=\sin(\pi)=0$; for $y=-4\sin(x)$, $y = 0$.
   • When $x=\frac{3\pi}{2}$, $y=\sin(\frac{3\pi}{2})=-1$; for $y=-4\sin(x)$, $y = 4$.
   • When $x = 2\pi$, $y=\sin(2\pi)=0$; for $y=-4\sin(x)$, $y = 0$.
   • We can use these key - points and the fact that the function is periodic with period $2\pi$ to graph the function over the interval $[-2\pi,2\pi]$. The negative sign in front of the $4$ reflects the graph of $y = 4\sin(x)$ about the $x$ - axis.

Answer:

The amplitude is 4.