Question

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.
$y = 4\sin(x)$
clear all draw:
period:
amplitude:
phase shift:
vertical shift:
question help: video ebook written example message instructor

Explanation:

Step1: Recall the general form of sine function

The general form of a sine function is \(y = A\sin(B(x - C))+D\), where \(A\) is the amplitude, \(\frac{2\pi}{|B|}\) is the period, \(C\) is the phase - shift, and \(D\) is the vertical shift.

Step2: Identify the values for the given function \(y = 4\sin(x)\)

For the function \(y = 4\sin(x)\), we can rewrite it as \(y=4\sin(1\times(x - 0))+0\).

• Amplitude:

The formula for amplitude is \(|A|\). Here, \(A = 4\), so the amplitude \(|A|=4\).

• Period:

The formula for the period is \(T=\frac{2\pi}{|B|}\). Since \(B = 1\), then \(T=\frac{2\pi}{|1|}=2\pi\).

• Phase - shift:

The formula for phase - shift is \(C\). Here, \(C = 0\), so there is no phase shift.

• Vertical - shift:

The formula for vertical - shift is \(D\). Here, \(D = 0\), so there is no vertical shift.

Answer:

Period: \(2\pi\)
Amplitude: \(4\)
Phase Shift: \(0\)
Vertical Shift: \(0\)