Question

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.
$y = 3\cos(x)$
clear all draw:
period:
amplitude:
phase shift:
vertical shift:

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 \(y = 3\cos(x)\), we can rewrite it as \(y=3\cos(1\times(x - 0))+0\), where \(A = 3\), \(B = 1\), \(C = 0\), \(D = 0\).

Step2: Calculate the period

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

Step3: Calculate the amplitude

The amplitude of a cosine function \(y = A\cos(B(x - C))+D\) is \(|A|\). Since \(A = 3\), the amplitude is \(|3| = 3\).

Step4: Calculate the phase - shift

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

Answer:

Period: \(2\pi\)
Amplitude: \(3\)
Phase Shift: \(0\)
Vertical Shift: \(0\)