Question

match the function with its graph.
$y = 2\sin(x)$
question help: video

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 the function \(y = 2\sin(x)\), we have \(A = 2\), \(B = 1\), \(C = 0\), and \(D = 0\).

Step2: Analyze the amplitude

The amplitude of a sine function \(y = A\sin(x)\) is given by \(|A|\). Here, \(A = 2\), so the amplitude is \(2\). This means the maximum value of the function is \(y = 2\) and the minimum value is \(y=- 2\).

Step3: Check key points

When \(x = 0\), \(y=2\sin(0)=0\). When \(x=\frac{\pi}{2}\), \(y = 2\sin(\frac{\pi}{2})=2\). When \(x=\pi\), \(y=2\sin(\pi)=0\). When \(x=\frac{3\pi}{2}\), \(y=2\sin(\frac{3\pi}{2})=-2\). When \(x = 2\pi\), \(y=2\sin(2\pi)=0\)

Answer:

The graph with amplitude \(2\) and passing through the points \((0,0)\), \((\frac{\pi}{2},2)\), \((\pi,0)\), \((\frac{3\pi}{2}, - 2)\), \((2\pi,0)\) is the correct match for \(y = 2\sin(x)\)