Question

1. which equation can be used to model the graph of the function shown?

a. ( y = sin 2x + 3 )
b. ( y = 2 sin x + 3 )
c. ( y = sin 2x - 3 )
d. ( y = 2 sin x - 3 )

Explanation:

Step1: Analyze the vertical shift

The general form of a sine function is \(y = A\sin(Bx)+C\). The vertical shift is given by \(C\). Looking at the graph, the mid - line is \(y = 3\). So \(C=3\). This rules out options \(c\) (\(C=-3\)) and \(d\) (\(C = - 3\)).

Step2: Analyze the period

The period of a sine function \(y=\sin(Bx)\) is \(T=\frac{2\pi}{B}\). For \(y = 2\sin(x)\), \(B = 1\) and \(T = 2\pi=360^{\circ}\). For \(y=\sin(2x)\), \(B = 2\) and \(T=\frac{2\pi}{2}=\pi = 180^{\circ}\). Looking at the graph, the period is \(180^{\circ}\).

Answer:

A. \(y=\sin(2x)+3\)