Question

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.
$y=-2\cos(x)$
clear all draw:
period (give exact answer):
amplitude:
phase shift:
vertical shift:
question help: video ebook written example message instructor

Explanation:

Step1: Recall the general form of cosine function

The general form of a cosine function is \(y = A\cos(B(x - C))+D\), where \(|A|\) is the amplitude, \(\frac{2\pi}{|B|}\) is the period, \(C\) is the phase - shift, and \(D\) is the vertical shift.
For the function \(y=-2\cos(x)\), we can rewrite it as \(y=-2\cos(1(x - 0))+0\).

Step2: Calculate the amplitude

The amplitude is \(|A|\). Here \(A=-2\), so \(|A| = 2\).

Step3: Calculate the period

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

Step4: Calculate the phase - shift

The phase - shift is \(C\). Here \(C = 0\).

Step5: Calculate the vertical shift

The vertical shift is \(D\). Here \(D = 0\).

Answer:

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