Question

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graph the given function. state the period, amplitude, phase shift, and vertica
$y = - 2 cos ( x )$
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Explanation:

Step1: Recall the general form of cosine function

The general form of a cosine function is \(y = A\cos(B(x - C))+D\). For the function \(y=- 2\cos(x)\), we have \(A=-2\), \(B = 1\), \(C = 0\), \(D=0\).

Step2: Calculate the amplitude

The amplitude of a cosine function \(y = A\cos(B(x - C))+D\) is given by \(|A|\). Here, \(A=-2\), so the amplitude \(|A|=| - 2|=2\).

Step3: Calculate the period

The period of a cosine function \(y = A\cos(B(x - C))+D\) is given by \(T=\frac{2\pi}{|B|}\). Since \(B = 1\), the period \(T=\frac{2\pi}{|1|}=2\pi\).

Step4: Calculate the phase - shift

The phase - shift of a cosine function \(y = A\cos(B(x - C))+D\) is given by \(C\). Here, \(C = 0\), so the phase - shift is \(0\).

Step5: Calculate the vertical shift

The vertical shift of a cosine function \(y = A\cos(B(x - C))+D\) is given by \(D\). Here, \(D = 0\), so the vertical shift is \(0\).

Answer:

Amplitude: \(2\), Period: \(2\pi\), Phase - shift: \(0\), Vertical shift: \(0\)