Question

unit trigonometry progress. the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. which of the following is the graph of $y = 3\sin 2x$? images of four graphs are shown

Explanation:

Step1: Recall the general form of a sine function

The general form of a sine function is \(y = A\sin(Bx - C)+D\). For \(y = 3\sin(2x)\), \(A = 3\), \(B=2\), \(C = 0\), \(D = 0\). The amplitude \(|A|\) gives the maximum value of the function. Here, the amplitude is \(|3|=3\). The period of the sine function \(y=\sin(Bx)\) is \(T=\frac{2\pi}{B}\). For \(y = 3\sin(2x)\), the period \(T=\frac{2\pi}{2}=\pi\).

Step2: Analyze each graph

• The first graph: It does not have the correct amplitude and period for \(y = 3\sin(2x)\).
• The second graph: The amplitude is \(3\) and the period is \(\pi\) (since within the \(x\) - range shown, the function repeats its pattern appropriately for \(B = 2\)).
• The third graph: The \(x\) - axis range is incorrect for the standard analysis of \(y=3\sin(2x)\) with the given \(y\) - axis and amplitude - period relationship.

Answer:

The second graph (the one with amplitude \(3\) and period \(\pi\) within the relevant \(x\) - range) is the graph of \(y = 3\sin(2x)\).