Question

which of the following statements about the graphed sine functio correct? (1 point) the domain of the graph is -3, 3. × the frequency of the graph is \\(\frac{1}{\pi}\\). the range of the graph is -\\(\pi\\), \\(\pi\\). the period of the graph is 2\\(\pi\\). incorrect domain describes the left and right behavior of the function, not the up and down behavior.

Explanation:

Step1: Analyze the domain of a sine function

The domain of \(y = \sin(x)\) is all real numbers, \(x\in(-\infty,\infty)\), not \([- 3,3]\).

Step2: Analyze the frequency formula

The general form of a sine function is \(y = A\sin(Bx - C)+D\), and the frequency \(f=\frac{B}{2\pi}\). For \(y = \sin(x)\), \(B = 1\), so \(f=\frac{1}{2\pi}
eq\frac{1}{\pi}\).

Step3: Analyze the range of a sine function

The range of \(y=\sin(x)\) is \([-1,1]\), not \([-\pi,\pi]\).

Step4: Analyze the period formula

The period of \(y = A\sin(Bx - C)+D\) is \(T=\frac{2\pi}{B}\). For \(y=\sin(x)\), \(B = 1\), so \(T = 2\pi\).

Answer:

The period of the graph is \(2\pi\).