Question

using degrees, choose the graph of $f(x)=2cos(3x)$

Explanation:

Step1: Find the amplitude

The general form of a cosine function is \(y = A\cos(Bx)\). For the function \(f(x)=2\cos(3x)\), the amplitude \(|A| = 2\). This means the graph oscillates between \(y = 2\) and \(y=- 2\).

Step2: Find the period

The period of the function \(y=\cos(Bx)\) is given by the formula \(T=\frac{360^{\circ}}{|B|}\). For the function \(f(x) = 2\cos(3x)\), where \(B = 3\), the period \(T=\frac{360^{\circ}}{3}=120^{\circ}\).

Since the amplitude is \(2\) (so the graph has a maximum value of \(2\) and a minimum value of \(-2\)) and the period is \(120^{\circ}\), the given graph (with amplitude \(2\) and period \(120^{\circ}\) as can be visually estimated from the x - axis markings) is the correct graph of \(y = 2\cos(3x)\)

Answer:

The provided graph is the correct graph of \(f(x)=2\cos(3x)\)